Two-layer multi-strand cables having very low, low and medium modulus

ABSTRACT

A two-layer multi-strand cord (60) has a modulus EC such that 50 GPa≤EC≤160 GPa. The cord comprises: (a) an internal layer (CI) of the cord made up of J&gt;1 internal strands (TI) wound in a helix having a modulus EI, each internal strand (TI) comprising: an internal layer (C1) made up of Q≥1 internal threads (F1), and an external layer (C2) made up of N&gt;1 external threads (F2) wound around the internal layer (C1), and (b) an external layer (CE) of the cord made up of L&gt;1 external strands (TE) wound around the internal layer (CI) of the cord, each external strand (TE) comprising: an internal layer (C1′) made up of Q′≥1 internal threads (F1′), and an external layer (C2′) made up of N′&gt;1 external threads (F2′) wound around the internal layer (C1′).

BACKGROUND

The invention relates to multi-strand cords that can be used notably forreinforcing tyres, particularly tyres for heavy industrial vehicles, andto tyres using such cords.

A tyre having a radial carcass reinforcement comprises a tread, twoinextensible beads, two sidewalls connecting the beads to the tread anda belt, or crown reinforcement, arranged circumferentially between thecarcass reinforcement and the tread. This crown reinforcement comprisesseveral reinforcements having different functions.

The crown reinforcement generally comprises a working reinforcementcomprising two working plies, or crossed plies, comprising filamentarymetal working reinforcing elements arranged substantially parallel toone another within each working ply, but crossed from one ply to theother, that is to say inclined, symmetrically or asymmetrically, withrespect to the median circumferential plane, by an angle generallyranging between 15 and 40°. This working reinforcement makes itpossible, included amongst other functions, for the transverse loadingsapplied by the ground to be transmitted at least partially to the tyrewhen the latter is running, so as to provide the tyre with steeringcapability, namely to give the tyre the ability to allow the vehicle towhich it is fitted to corner.

Such filamentary metal working elements are notably described inWO2008026271. WO2008026271 describes two-layer multi-strand cordscomprising an internal layer of the cord made up of J>1 internal strandswound in a helix and an external layer of the cord made up of L>1external strands wound around the internal layer of the cord. Eachinternal and external strand has multiple layers and comprises at leastan internal layer made up of Q>1 internal threads, possibly anintermediate layer made up of P>1 intermediate threads wound around theinternal layer, and an external layer made up of N>1 external threadswound around the internal or intermediate layer.

In WO2008026271, the objective is to provide filamentary workingreinforcing elements that have a stiffness and a breaking strength thatare as high as possible so as to avoid the damage caused to the crownreinforcement, and notably to the working reinforcement, by theobstacles encountered by the tyre when it is running.

In WO2008026271, this objective is achieved by increasing the number ofinternal strands and external strands as far as possible with respect toconventional multi-strand cords in which the breaking strength is lowerand for which J=1 and L=6, such as notably described in WO2015090920.Thus, in WO2008026271, the objective is to combat the deformationimposed by the obstacles encountered by countering them with cords thatare as stiff and mechanically strong as possible.

However, while this solution is effective against obstacles ofrelatively small or medium size, it proves ineffective with regard tolarger-sized obstacles. Specifically, in such cases, the loadingsexerted on the cords are higher than the hardness of the steel and theobstacle therefore shears through the cords, and the stiffer these cordsare, and the better they oppose the deformation imposed by the obstacle,the more easily they become sheared.

One object of the invention is a cord that makes it possible to avoidthe damage caused by obstacles that highly stress the crownreinforcement, notably the working reinforcement of the tyre.

SUMMARY

Cord According to the Invention

To this end, one subject of the invention is a two-layer multi-strandcord having a modulus EC and comprising:

-   -   an internal layer of the cord made up of J>1 internal strands        wound in a helix having a modulus EI, each internal strand        comprising:        -   an internal layer made up of Q≥1 internal threads, and        -   an external layer made up of N>1 external threads wound            around the internal layer,    -   an external layer of the cord made up of L>1 external strands        wound around the internal layer of the cord, each external        strand comprising:        -   an internal layer made up of Q′≥1 internal threads,        -   an external layer made up of N′>1 external threads wound            around the internal layer,            in which cord 50 GPa≤EC≤160 GPa.

Unlike in the prior art in which the cords have modulus values muchhigher than 160 GPa and are therefore relatively stiff, the inventorshave found that the cords according to the invention, with lower modulusvalues, perform better against obstacles that highly stress the crownreinforcement of the tyre.

Specifically, the inventors have found that it was more effective to hugthe obstacle by using a cord with a lower modulus than to attempt tostiffen and reinforce the cords as far as possible in order to opposethe deformations imposed by the obstacles as was taught in the priorart. By hugging the obstacles, the shearing imposed on the cords andtherefore the risk of breakage of these cords is reduced.

The value of the modulus EC of the cords according to the inventionensures that the latter have structures corresponding to relatively lowmodulus values varying between 50 GPa and 160 GPa, thus making itpossible to hug the obstacles encountered, unlike the cords of the priorart which are far too stiff.

Furthermore, the value of the modulus EC of the cords according to theinvention ensures that the latter have a modulus that is high enough toprovide the tyre with sufficient steering capability when used in theworking reinforcement.

In the invention, the cord has two layers of strands, which means to saythat it comprises an assembly made up of two layers of strands, neithermore nor less, which means to say that the assembly has two layers ofstrands, not one, not three, but only two. The external layer of thecord is wound in a helix around the internal layer of the cord incontact with the internal layer of the cord.

Furthermore, unlike in the case where J=1 and in which there might be arisk of seeing the internal strand exit the cord radially under theeffect of the repeated compressive loadings applied to the cord, thepresence of several strands in the internal layer of the cord (J>1)wound in a helix makes it possible to reduce this risk, the compressiveloadings then being distributed over the plurality of strands of theinternal layer of the cord and the helix keeping the internal strandstogether.

As an option and a preference, in one embodiment, the cord does not haveany polymeric compound, notably the cord does not have any sheath of anypolymeric compound covering the internal strand. In another embodiment,the cord does not have any elastomeric compound, notably the cord doesnot have any sheath of any elastomeric compound covering the internallayer of the cord.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be better understood on reading the followingdescription, given solely by way of non-limiting example and withreference to the drawings, in which:

FIG. 1 is a view in cross section perpendicular to the circumferentialdirection of a tyre according to the invention;

FIG. 2 is a detail view of the region II of FIG. 1 ;

FIG. 3 is a schematic view in cross section perpendicular to the axis ofthe cord (which is assumed to be straight and at rest) of a cordaccording to a first embodiment of the invention;

FIG. 4 is a graph illustrating the force—elongation curve for the cordof FIG. 3 according to the first embodiment;

FIG. 5 is a graph similar to that of FIG. 4 of a cord according to asecond embodiment;

FIG. 6 is a view similar to that of FIG. 3 of a cord according to athird embodiment of the invention;

FIG. 7 is a graph similar to that of FIG. 4 of the cord according to thethird embodiment; and

FIGS. 8, 9 and 10 are views similar to that of FIG. 3 of cordsrespectively according to eighth, fifteenth and twenty-secondembodiments.

DETAILED DESCRIPTION

What is meant by a polymer compound or a polymeric compound is that thecompound contains at least one polymer. For preference, such a polymermay be a thermoplastic, for example a polyester or a polyamide, athermosetting polymer, an elastomer, for example natural rubber, athermoplastic elastomer or a combination of these polymers.

What is meant by an elastomer compound or an elastomeric compound isthat the compound contains at least one elastomer or one rubber (the twoterms being synonyms) and at least one other component. For preference,the elastomer compound also contains a vulcanization system and afiller. More preferentially, the elastomer is a diene elastomer.

In the description and the claims, any range of values denoted by theexpression “between a and b” represents the range of values extendingfrom more than a to less than b (namely excluding the end-points a andb), whereas any range of values denoted by the expression “from a to b”means the range of values extending from the end-point “a” as far as theend-point “b”, namely including the strict end-points “a” and “b”.

It will be recalled that, as is known, the pitch of a strand representsthe length of this strand, measured parallel to the axis of the cord,after which the strand that has this pitch has made a complete turnaround the said axis of the cord. Similarly, the pitch of a threadrepresents the length of this thread, measured parallel to the axis ofthe strand in which it is located, after which the thread that has thispitch has made a complete turn around the said axis of the strand.

What is meant by the direction of winding of a layer of strands or ofthreads is the direction that the strands or the threads form withrespect to the axis of the cord or of the strand. The direction ofwinding is commonly designated by the letter Z or S.

The pitches, directions of winding, and diameters of the threads and ofthe strands are determined in accordance with standard ASTM D2969-04 of2014. The radii of winding are measured by using a microscope to look ata cross section of the cord taken on an axis perpendicular to the axisof the cord.

What is meant by similar thread diameters is that the ratios of thediameters of the threads considered in pairs range from 0.75 to 1.25.What is meant by identical thread diameters is that the ratios of thediameters of the threads considered in pairs are equal to 1.

Advantageously, the cord is made of metal. What is meant by metal cordis, by definition, a cord formed of threads made entirely (100% of thethreads) of a metallic material. Such a metal cord is preferentiallyimplemented with threads made of steel, more preferentially of pearlitic(or ferritic-pearlitic) carbon steel referred to as “carbon steel”below, or else made of stainless steel (by definition, steel comprisingat least 11% chromium and at least 50% iron). However, it is of coursepossible to use other steels or other alloys.

When a carbon steel is advantageously used, its carbon content (% byweight of steel) is preferably comprised between 0.2% and 1.2%, notablybetween 0.5% and 1.1%; these contents represent a good compromisebetween the mechanical properties required for the tyre and theworkability of the threads.

The metal or the steel used, whether in particular it is a carbon steelor a stainless steel, may itself be coated with a metal layer whichimproves, for example, the workability properties of the metal cordand/or of its constituent elements, or the use properties of the cordand/or of the tyre themselves, such as the properties of adhesion,corrosion resistance or resistance to ageing. According to one preferredembodiment, the steel used is covered with a layer of brass (Zn—Cualloy) or of zinc.

For preference, the threads of the one same layer of a predetermined(internal or external) strand all have substantially the same diameter.Advantageously, the internal strands all have substantially the samediameter. Advantageously, the external strands all have substantiallythe same diameter. What is meant by “substantially the same diameter” isthat the threads or the strands have identical diameters to within theindustrial tolerances.

In the present application, the modulus EC of a cord is calculated bymeasuring the gradient of the elastic portion of a force-elongationcurve obtained by applying standard ASTM D2969-04 of 2014 to the cordtested, and then by apportioning this gradient to the metal crosssection of the cord, namely the sum of the cross sections of the threadsthat make up the cord. Alternatively, the metal cross section can bedetermined by measuring the linear mass of the cord in accordance withstandard ASTM D2969-04 of 2014, and by dividing this linear mass by thedensity of the steel used.

The elastic portion of the curve corresponds to a substantially linearportion of the force-elongation curve, which portion compliments thestructural portion and the plastic portion of the force-elongationcurve. The elastic portion corresponds to an elastic elongation Ae andis the result of the construction of the cord, notably of the angles ofthe various layers and of the diameters of the threads. The elasticportion, and the corresponding elongation Ae, of the force-elongationcurve are notably described in documents U.S. Pat. No. 5,843,583, WO2005/014925 and WO2007/090603 and correspond to the portion and to theelongation of the force-elongation curve comprised between:

-   -   the structural portion corresponding to the structural        elongation As, resulting from the aeration of the cord, namely        the empty space between the various threads or strands that make        up the cord, and    -   the plastic portion corresponding to the plastic elongation Ap,        resulting from the plasticity (irreversible deformation beyond        the elastic limit) of one or more threads of the cord.

For certain cords, there is no aeration in the cord, which means thatthe structural elongation As is zero. In all cases (As zero and Asnon-zero), the elastic portion corresponds to the linear portion of theforce-elongation curve that has the steepest gradient.

The modulus EC of the cord is measured on an as-manufactured cord,namely a cord without any elastomeric compound in which the cord wouldbe embedded in order to form a ply. Similarly, the modulus EI of theinternal layer of the cord is measured by taking the internal layer ofthe cord either as-manufactured or by unravelling the external layer ofexternal strands from the finished cord in order to obtain the internallayer of the cord alone. As an alternative, the modulus values EC and EIcould be measured by extracting a cord from a tyre and removing all theelastomeric compound from around and within the cord, for example bychemical derubberizing as is well known to those skilled in the art.

The following description will also adopt the following definitions forthe helix angle α of each internal strand in the internal layer of thecord and the helix angle α′ of each external strand in the externallayer of the cord.

$\alpha = {\arctan\left( \frac{2\pi\;{RI}}{PI} \right)}$in which RI is the radius of winding of the internal strands, and PI isthe pitch at which each internal strand is wound.

$\alpha^{\prime} = {\arctan\left( \frac{2\pi\;{RE}}{PE} \right)}$in which RE is the radius of winding of the external strands, and PE isthe pitch at which each external strand is wound.

The radii of winding RI and RE are measured on a transverse crosssection perpendicular to the main axis of the cord and correspond to thedistance between the centre of the helix described by each internal andexternal strand and the centre of the cord, respectively.

In one embodiment in which each internal strand has two layers, thefollowing description will also adopt the following definitions for thehelix angle β of each internal thread in the internal layer within eachinternal strand and the helix angle γ of each external thread in theexternal later within each internal strand.

$\beta = {\arctan\left( \frac{2\pi\; R\; 1}{p1} \right)}$in which R1 is the radius of winding of the Q internal threads of eachinternal strand, and p1 is the pitch at which the Q internal threads areassembled within each internal strand. Where Q=1, R1=0 and thereforeβ=0.

$\gamma = {\arctan\left( \frac{2\pi\; R\; 2}{p2} \right)}$in which R2 is the radius of winding of the N external threads of eachinternal strand, and p2 is the pitch at which the N external threads areassembled within each internal strand.

In this embodiment, each internal thread has a diameter D1 and eachexternal thread has a diameter D2. The radii of winding R1 and R2 aremeasured on a transverse cross section perpendicular to the main axis ofeach internal strand considered individually and correspond to thedistance between the centre of the helix described by each internal andexternal thread and the centre of the internal strand, respectively.

In one embodiment in which each internal strand has three layers, thefollowing description will also adopt the following definitions for thehelix angle β of each internal thread in the internal layer within eachinternal strand, the helix angle δ of each intermediate thread in theintermediate layer within each internal strand, and the helix angle γ ofeach external thread in the external layer within each internal strand.

$\beta = {\arctan\left( \frac{2\pi\; R\; 1}{p1} \right)}$in which R1 is the radius of winding of the Q internal threads of eachinternal strand, and p1 is the pitch at which the Q internal threads areassembled within each internal strand. Where Q=1, R1=0 and thereforeβ=0.

$\delta = {\arctan\left( \frac{2\pi\; R\; 2}{p2} \right)}$in which R2 is the radius of winding of the P intermediate threads ofeach internal strand, and p2 is the pitch at which the P intermediatethreads are assembled within each internal strand.

$\gamma = {\arctan\left( \frac{2\pi\; R\; 3}{p3} \right)}$in which R3 is the radius of winding of the N external threads of eachinternal strand, and p3 is the pitch at which the N external threads areassembled within each internal strand. The radii of winding R1, R2 andR3 are measured on a transverse cross section perpendicular to the mainaxis of each internal strand considered individually and correspond tothe distance between the centre of the helix described by each internal,intermediate and external thread and the centre of the internal strand,respectively.

In this embodiment, each internal thread has a diameter D1, eachintermediate thread has a diameter D2, and each external thread has adiameter D3.

In one embodiment in which each external strand has two layers, thefollowing description will also adopt the following definitions for thehelix angle β of each internal thread in the internal layer within eachexternal strand and the helix angle γ′ of each external thread in theexternal layer within each external strand.

$\beta^{\prime} = {\arctan\left( \frac{2\pi\; R\; 1^{\prime}}{p\; 1^{\prime}} \right)}$in which R1′ is the radius of winding of the Q′ internal threads of eachexternal strand, and p1′ is the pitch at which the Q′ internal threadsare assembled within each external strand. Where Q′=1, R1′=0 andtherefore β′=0.

$\gamma^{\prime} = {\arctan\left( \frac{2\pi\; R\; 2^{\prime}}{p\; 2^{\prime}} \right)}$in which R2′ is the radius of winding of the N′ external threads of eachexternal strand, and p2′ is the pitch at which the N′ external threadsare assembled within each external strand.

In this embodiment, each internal thread has a diameter D1′ and eachexternal thread has a diameter D2′. The radii of winding R1′ and R2′ aremeasured on a transverse cross section perpendicular to the main axis ofeach external strand considered individually and correspond to thedistance between the centre of the helix described by each internal andexternal thread and the centre of the external strand, respectively.

In one embodiment in which each external strand has three layers, thefollowing description will also adopt the following definitions for thehelix angle β of each internal thread in the internal layer within eachexternal strand, the helix angle δ′ of each intermediate thread in theintermediate layer within each external strand, and the helix angle γ′of each external thread in the external layer within each externalstrand.

$\beta^{\prime} = {\arctan\left( \frac{2\pi\; R\; 1^{\prime}}{p\; 1^{\prime}} \right)}$in which R′ is the radius of winding of the Q′ internal threads of eachexternal strand, and p1′ is the pitch at which the Q′ internal threadsare assembled within each external strand. Where Q′=1, R1′=0 andtherefore β′=0.

$\delta^{\prime} = {\arctan\left( \frac{2\pi\; R\; 2^{\prime}}{p\; 2^{\prime}} \right)}$in which R2′ is the radius of winding of the P′ intermediate threads ofeach external strand, and p2′ is the pitch at which the P′ intermediatethreads are assembled within each external strand.

$\gamma^{\prime} = {\arctan\left( \frac{2\pi\; R\; 3^{\prime}}{p\; 3^{\prime}} \right)}$n which R3′ is the radius of winding of the N′ external threads of eachexternal strand, and p3′ is the pitch at which the N′ external threadsare assembled within each external strand prior to the assembling of theinternal strands and of the external strands with one another.

In this embodiment, each internal thread has a diameter D1′, eachintermediate thread has a diameter D2′, and each external thread has adiameter D3′. The radii of winding R1′, R2′ and R3′ are measured on atransverse cross section perpendicular to the main axis of each externalstrand considered individually and correspond to the distance betweenthe centre of the helix described by each internal, intermediate andexternal thread and the centre of the external strand, respectively.

In preferred embodiments, with the internal layer of the cord having amodulus EI, 25 GPa≤EI≤180 GPa, preferably 36 GPa≤EI≤180 GPa.

As the cords according to the invention have an architecture in whichJ>1, the most severe transverse loadings applied to the cord when thelatter is tensioned are the transverse loadings applied between theinternal strands, notably in instances in which the external layer ofthe cord is desaturated, unlike a cord in which J=1 and in which themost severe transverse loadings are the transverse loadings applied bythe external strands to the internal strands, notably in instances inwhich the external layer of the cord is desaturated.

Ina first variant in which the internal layer of the cord has arelatively low modulus, with the internal layer of the cord having amodulus EI, 25 GPa≤EI≤94 GPa, preferably 36 GPa≤EI≤94 GPa. Thus, thelower the modulus of the internal layer, the better the principalloadings will be reacted and the better the breaking strength of thecord will be. The breaking strength of the cord is maximized here byusing a relatively low modulus for the internal layer. In one particularvariant, 25 GPa≤EI≤102 GPa, preferably 36 GPa≤EI≤102 GPa.

In a second variant in which the internal layer of the cord has a highermodulus, with the internal layer of the cord having a modulus EI, 95GPa≤EI≤180 GPa.

In an embodiment in which the internal layer of the cord and the cordhave relatively similar modulus values, 0.60≤EC/EI≤1.20. In thisembodiment, the inventors are postulating the hypothesis that the coreand the layer work more or less together when the cord is stressed,notably in tension. In this way, the compromise between the breakingstrength of the cord and its resistance to cutting is maximized.

In another embodiment in which the internal layer of the cord and thecord have relatively different modulus values, EC/EI≤0.59 or 1.21≤EC/EI.

In a variant, the internal layer of the cord has a relatively highmodulus with respect to the modulus of the cord, namely EC/EI≤0.59,preferably 0.40≤EC/EI≤0.59. This variant favours the resistance of thecord to cutting over its breaking strength.

In another variant, the internal layer of the cord has a relatively lowmodulus with respect to the modulus of the cord, namely 1.21≤EC/EI,preferably 1.21≤EC/EI≤3.00. This variant favours the breaking strengthof the cord over its resistance to cutting.

In preferred embodiments of the invention, the cords have the followingadvantageous structural characteristics.

In one preferred embodiment, the helix angle α of each internal strandin the internal layer of the cord ranges:

-   -   from 7° to 38° in an embodiment using internal strands and        external strands having two layers,    -   from 4° to 41° in an embodiment using internal strands and        external strands having three layers,    -   from 3° to 36° in an embodiment using internal strands having        two layers and external strands having three layers,    -   from 4° to 36° in an embodiment using internal strands having        three layers and external strands having two layers.

In that particular variant, the helix angle α of each internal strand inthe internal layer of the cord ranges from 5° to 42°.

By controlling chiefly the value of the helix angle α, the value of themodulus associated with the internal layer of the cord is largelycontrolled. This is because the helix angle α plays a predominant roleby comparison with the angles of the threads of the layers whosecontribution to the modulus is smaller. Thus, the higher the helix angleα of each internal strand, the lower the modulus associated with theinternal layer. Thus, advantageously, the internal strands are wound ina helix with a pitch PI ranging from 10 mm to 65 mm, preferably from 10mm to 45 mm.

In one preferred embodiment, the helix angle α′ of each external strandin the external layer of the cord ranges:

-   -   from 7° to 38° in an embodiment using internal strands and        external strands having two layers,    -   from 13° to 36° in an embodiment using internal strands and        external strands having three layers,    -   from 10° to 34° in an embodiment using internal strands having        two layers and external strands having three layers,    -   from 10° to 32° in an embodiment using internal strands having        three layers and external strands having two layers.

In that particular variant, the helix angle α of each internal strand inthe internal layer of the cord ranges from 10° to 32°.

In a similar way to the helix angle α, by controlling chiefly the valueof the helix angle α′, the value of the modulus associated with theexternal layer of the cord is largely controlled. This is because thehelix angle α′ plays a predominant role by comparison with the angles ofthe threads of the layers whose contribution to the modulus is smaller.Thus, the higher the helix angle α′ of each external strand, the lowerthe modulus associated with the external layer.

Advantageously, the L external strands are wound in a helix with a pitchPE ranging from 30 mm to 65 mm, preferably from 30 mm to 60 mm.

In the particular variant using internal strands having two layers,20°≤2α+β+γ≤136°.

In the particular variant using internal strands having three layers,50°≤3α+β+γ+γ′80.

In the particular variant using external strands having two layers,39°≤2α′+β′+γ≤100°.

In the particular variant using external strands having three layers,65°≤3α′+β′+δ′+γ′≤95°.

In the embodiment using internal strands and external strands having twolayers, 11°≤2α+β+γ≤110°, and

-   -   in an embodiment in which Q=1, advantageously 11°≤2α+β+γ≤74°,        and    -   in an embodiment in which Q>1, advantageously 16°≤2α+β+γ≤110°.

In an embodiment using internal strands and external strands havingthree layers, 25°≤3α+β+δ+γ≤158°, and

-   -   in an embodiment in which Q=1, advantageously 25°≤3α+β+γ+γ≤140°,        and    -   in an embodiment in which Q>1, advantageously 36°≤3α+β+δ+γ≤158°.

In an embodiment using internal strands having two layers and externalstrands having three layers, 16°≤2α+β+γ≤105°, and

-   -   in an embodiment in which Q=1, advantageously 16°≤2α+β+γ≤86°,        and    -   in an embodiment in which Q>1, advantageously 20°≤2α+β+γ≤105°.

In an embodiment using internal strands having three layers and externalstrands having two layers, 26°≤3α+β+δ+γ≤:162°, and

-   -   in an embodiment in which Q=1, advantageously 26°≤3α+β+γ+γ≤140°,        and    -   in an embodiment in which Q>1, advantageously 36°≤3α+β+δ+γ≤162°.

In the embodiment using internal strands and external strands having twolayers, 23°≤2α′+β′+γ′≤97°, and

-   -   in an embodiment in which Q′=1, advantageously        23°≤2α′+β′+γ′≤85°, and    -   in an embodiment in which Q′>1, advantageously        28°≤2α′+β′+γ′≤97°.

In an embodiment using internal strands and external strands havingthree layers, 48°≤3α′+β′+δ′+γ′≤154°, and

-   -   in an embodiment in which Q′=1, advantageously        48°≤3α′+β′+δ′+γ′≤145°, and    -   in an embodiment in which Q′>1, advantageously        61°≤3α′+β′+δ′+γ′≤154°.

In an embodiment using internal strands having two layers and externalstrands having three layers, 47° 3α′+β′+δ′+γ′≤147°, and

-   -   in an embodiment in which Q′=1, advantageously        47°≤3α′+β′+δ′+γ′≤147°, and    -   in an embodiment in which Q′>1, advantageously        62°≤3α′+β′+δ′+γ′≤140°.

In an embodiment using internal strands having three layers and externalstrands having two layers, 28°≤2α′+β′+γ′≤96°, and

-   -   in an embodiment in which Q′=1, advantageously        28°≤2α′+3′+γ′≤86°.    -   in an embodiment in which Q′>1, advantageously        34°≤2α′+β′+γ′≤96°.

In an embodiment using internal strands and external strands having twolayers, 28°≤2α′+β′+γ′≤96°. In an embodiment in which Q′=1,advantageously 28°≤2α′+β′+γ′≤86°.

In an embodiment in which Q′>1, advantageously 34°≤2α′+β′+γ′≤96°. Inthat particular variant, 73°≤2α+β+γ+2α′+β′+γ′≤195°.

In an embodiment using internal strands and external strands havingthree layers, 84°≤3α+β+γ+γ+3α′+β′+δ′+γ′≤280°. In an embodiment in whichQ=1 and Q′=1, advantageously 84°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤246°. In anembodiment in which Q>1 and Q′=1, advantageously96°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤261°. In an embodiment in which Q=1 and Q′>1,advantageously 88°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤254°. In an embodiment in whichQ>1 and Q′>1, advantageously 101°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤280°. In thatparticular variant, 130°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤170°.

In an embodiment using internal strands having two layers and externalstrands having three layers, 84°≤2α+β+γ+3α′+β′+δ′+γ′≤226°. In anembodiment in which Q=1 and Q′=1, advantageously84°≤2α+β+γ+3α′+β′+δ′+γ′≤199°. In an embodiment in which Q>1 and Q′=1,advantageously 88°≤2α+β+γ+3α′+β′+δ′+γ′≤206°. In an embodiment in whichQ=1 and Q′>1, advantageously 96°≤2α+β+γ+3α′+β′+δ′+γ′≤214°. In anembodiment in which Q>1 and Q′>1, advantageously99°≤2α+β+γ+3α′+β′+γ′+γ′≤226°. In that particular variant,110°≤2α+β+γ+3α′+β′+δ′+γ′≤150°.

In an embodiment using internal strands having three layers and externalstrands having two layers, 64°≤3α+β+δ+γ+2α′+β′+γ′≤224°. In an embodimentin which Q=1 and Q′=1, advantageously 64°≤3α+β+δ+γ+2α′+β′+γ′≤200°. In anembodiment in which Q>1 and Q′=1, advantageously73°≤3α+β+δ+γ+2α′+β′+γ′≤212°. In an embodiment in which Q=1 and Q′>1,advantageously 68°≤3α+β+δ+γ+2α′+β′+γ′≤220°. In an embodiment in whichQ>1 and Q′>1, advantageously 80°≤3α+β+δ+γ+2α′+β′+γ′≤224°. In thatparticular variant, 110°≤3α+β+γ+γ+2α′+β′+γ′≤150°.

For identical or similar diameters of threads used, the angles thusdefined make it possible to structurally define a cord according to theinvention that is easy to manufacture on an industrial scale by alteringonly the helix angles α, α′, β, β′, δ, δ′, γ and γ′.

In an embodiment using internal strands and external strands having twolayers:

-   -   When Q>1, the helix angle β of each internal thread in the        internal layer within each internal strand ranges from 4° to        25°, preferably 4° to 17°. Advantageously, the Q internal        threads of each internal strand are assembled within each        internal strand at a pitch p1 ranging from 2 to 20 mm,        preferably from 5 to 20 mm.    -   When Q=1, the helix angle γ of each external thread in the        external layer within each internal strand ranges from 6° to        31°, preferably from 5° to 26°. Advantageously, the N external        threads of each internal strand are assembled within each        internal strand at a pitch p2 ranging from 4 to 40 mm,        preferably from 5 to 30 mm.    -   When Q>1, the helix angle γ of each external thread in the        external layer within each internal strand ranges from 5° to        31°. Advantageously, the N external threads of each internal        strand are assembled within each internal strand at a pitch p2        ranging from 4 to 40 mm.    -   When Q′>1, the helix angle β of each internal thread in the        internal layer within each external strand ranges from 4° to        25°, preferably from 4° to 17°. Advantageously, the Q′ internal        threads of each external strand are assembled within each        external strand at a pitch p1′ ranging from 2 to 20 mm,        preferably from 5 to 20 mm.    -   When Q=1, the helix angle γ′ of each external thread in the        external layer within each external strand ranges from 6° to        31°, preferably from 5° to 26°. Advantageously, the N′ external        threads of each internal strand are assembled within each        external strand at a pitch p2′ ranging from 4 to 40 mm,        preferably from 5 to 30 mm.    -   When Q>1, the helix angle γ′ of each external thread in the        external layer within each external strand ranges from 5° to        31°. Advantageously, the N′ external threads of each internal        strand are assembled within each external strand at a pitch p2′        ranging from 4 to 40 mm.    -   In that particular variant:        -   i. if Q>1, β ranges from 4° to 25° and p1 ranges from 2 to            20 mm,        -   ii. γ ranges from 6° to 31° and p2 ranges from 4 to 40 mm,        -   iii. if Q′>1, β′ ranges from 4° to 25° and p1 ranges from 2            to 20 mm,        -   iv. γ′ ranges from 6° to 31° and p2 ranges from 4 to 40 mm.

In an embodiment using internal strands and external strands havingthree layers:

-   -   When Q>1, the helix angle β of each internal thread in the        internal layer within each internal strand ranges from 4° to        17°. Advantageously, when Q>1, the Q internal threads of each        internal strand are assembled within each internal strand at a        pitch p1 ranging from 5 to 15 mm. When Q=1, the helix angle δ of        each intermediate thread in the intermediate layer within each        internal strand ranges from 6° to 30°. Advantageously, the P        intermediate threads of each internal strand are assembled        within each internal strand at a pitch p2 ranging from 5 to 20        mm.    -   When Q>1, the helix angle δ of each intermediate thread in the        intermediate layer within each internal strand ranges from 8° to        22°. Advantageously, the P intermediate threads of each internal        strand are assembled within each internal strand at a pitch p2        ranging from 10 to 20 mm.    -   When Q=1, the helix angle γ of each external thread in the        external layer within each internal strand ranges from 7° to        30°. Advantageously, the N external threads of each internal        strand are assembled within each internal strand at a pitch p3        ranging from 10 to 40 mm.    -   When Q>1, the helix angle γ of each external thread in the        external layer within each internal strand ranges from 9° to        25°. Advantageously, the N external threads of each internal        strand are assembled within each internal strand at a pitch p3        ranging from 10 to 40 mm.    -   When Q′>1, the helix angle β′ of each internal thread in the        internal layer within each external strand ranges from 4° to        20°. Advantageously, the Q′ internal threads of each external        strand are assembled within each external strand at a pitch p1′        ranging from 5 to 15 mm.    -   When Q′=1, the helix angle δ′ of each intermediate thread in the        intermediate layer within each external strand ranges from 6° to        22°. Advantageously, the P′ intermediate threads of each        external strand are assembled within each external strand at a        pitch p2′ ranging from 5 to 20 mm.    -   When Q′>1, the helix angle δ′ of each intermediate thread in the        intermediate layer within each external strand ranges from 8° to        22°. Advantageously, the P′ intermediate threads of each        external strand are assembled within each external strand at a        pitch p2′ ranging from 10 to 20 mm.    -   When Q′=1, the helix angle γ′ of each external thread in the        external layer within each external strand ranges from 7° to        22°. Advantageously, the N′ external threads of each external        strand are assembled within each external strand at a pitch p3′        ranging from 10 to 40 mm.    -   When Q′>1, the helix angle γ′ of each external thread in the        external layer within each external strand ranges from 9° to        25°. Advantageously, the N′ external threads of each external        strand are assembled within each external strand at a pitch p3′        ranging from 10 to 40 mm.    -   In that particular variant:        -   i. if Q>1, β ranges from 7° to 17° and p1 ranges from 1 to            10 mm,        -   ii. δ ranges from 7° to 17° and p2 ranges from 2 to 20 mm,        -   iii. γ ranges from 7° to 17° and p3 ranges from 4 to 40 mm,        -   iv. if Q′>1, β′ ranges from 10° to 20° and p1′ ranges from 1            to 10 mm,        -   v. δ′ ranges from 10° to 20° and p2′ ranges from 2 to 20 mm,        -   vi. γ′ ranges from 10° to 20° and p3′ ranges from 4 to 40            mm.

In an embodiment using internal strands having two layers and externalstrands having three layers:

-   -   When Q>1, the helix angle β of each internal thread in the        internal layer within each internal strand ranges from 4° to        17°. Advantageously, when Q>1, the Q internal threads of each        internal strand are assembled within each internal strand at a        pitch p1 ranging from 5 to 20 mm.    -   When Q>1, the helix angle γ of each external thread in the        external layer within each internal strand ranges from 7° to        20°. Advantageously, the N external threads of each internal        strand are assembled within each internal strand at a pitch p2        ranging from 5 to 40 mm.    -   When Q=1, the helix angle γ of each external thread in the        external layer within each internal strand ranges from 5° to        26°. Advantageously, the N external threads of each internal        strand are assembled within each internal strand at a pitch p2        ranging from 5 to 30 mm.    -   When Q′>1, the helix angle β′ of each internal thread in the        internal layer within each external strand ranges from 4° to        20°. Advantageously, the Q′ internal threads of each external        strand are assembled within each external strand at a pitch p1′        ranging from 5 to 15 mm.    -   When Q′=1, the helix angle δ′ of each intermediate thread in the        intermediate layer within each external strand ranges from 6° to        22°. Advantageously, the P′ intermediate threads of each        external strand are assembled within each external strand at a        pitch p2′ ranging from 5 to 20 mm.    -   When Q′>1, the helix angle δ′ of each intermediate thread in the        intermediate layer within each external strand ranges from 8° to        22°. Advantageously, the P′ intermediate threads of each        external strand are assembled within each external strand at a        pitch p2′ ranging from 10 to 20 mm.    -   When Q′=1, the helix angle γ′ of each external thread in the        external layer within each external strand ranges from 7° to        22°. Advantageously, the N′ external threads of each external        strand are assembled within each external strand at a pitch p3′        ranging from 10 to 40 mm.    -   When Q′>1, the helix angle γ′ of each external thread in the        external layer within each external strand ranges from 9° to        25°. Advantageously, the N′ external threads of each external        strand are assembled within each external strand at a pitch p3′        ranging from 10 to 40 mm.    -   In that particular variant:        -   i. If Q>1, β ranges from 7° to 17° and p1 ranges from 2 to            20 mm,        -   ii. γ ranges from 7° to 17° and p2 ranges from 4 to 40 mm,        -   iii. If Q′>1, β′ ranges from 10° to 20° and p1′ ranges from            1 to 10 mm,        -   iv. δ′ ranges from 10° to 20° and p2′ ranges from 2 to 20            mm,        -   v. γ′ ranges from 10° to 20° and p3′ ranges from 4 to 40 mm.

In an embodiment using internal strands having three layers and externalstrands having two layers:

-   -   When Q>1, the helix angle β of each internal thread in the        internal layer within each internal strand ranges from 4° to        17°. Advantageously, when Q>1, the Q internal threads of each        internal strand are assembled within each internal strand at a        pitch p1 ranging from 5 to 15 mm.    -   When Q=1, the helix angle δ of each intermediate thread in the        intermediate layer within each internal strand ranges from 6° to        30°. Advantageously, the P intermediate threads of each internal        strand are assembled within each internal strand at a pitch p2        ranging from 5 to 20 mm.    -   When Q>1, the helix angle δ of each intermediate thread in the        intermediate layer within each internal strand ranges from 8° to        22°. Advantageously, the P intermediate threads of each internal        strand are assembled within each internal strand at a pitch p2        ranging from 10 to 20 mm.    -   When Q=1, the helix angle γ of each external thread in the        external layer within each internal strand ranges from 7° to        30°. Advantageously, the N external threads of each internal        strand are assembled within each internal strand at a pitch p3        ranging from 10 to 40 mm.    -   When Q>1, the helix angle γ of each external thread in the        external layer within each internal strand ranges from 9° to        25°. Advantageously, the N external threads of each internal        strand are assembled within each internal strand at a pitch p3        ranging from 10 to 40 mm.    -   When Q′>1, the helix angle β′ of each internal thread in the        internal layer within each external strand ranges from 4° to        17°. Advantageously, the Q′ internal threads of each external        strand are assembled within each external strand at a pitch p1′        ranging from 5 to 20 mm. When Q′>1, the helix angle γ′ of each        external thread in the external layer within each external        strand ranges from 7° to 20°. Advantageously, the N′ external        threads of each external strand are assembled within each        external strand at a pitch p2′ ranging from 5 to 40 mm.    -   When Q′=1, the helix angle γ′ of each external thread in the        external layer within each external strand ranges from 5° to        26°. Advantageously, the N′ external threads of each external        strand are assembled within each external strand at a pitch p2′        ranging from 5 to 30 mm.    -   In that particular variant:        -   i. If Q>1, β ranges from 7° to 17° and p1 ranges from 1 to            10 mm,        -   ii. δ ranges from 7° to 17° and p2 ranges from 2 to 20 mm,        -   iii. γ ranges from 7° to 17° and p3 ranges from 4 to 40 mm,        -   iv. If Q′>1, β′ ranges from 7° to 17° and p1′ ranges from 2            to 20 mm,        -   v. γ′ ranges from 7° to 17° and p2′ ranges from 4 to 40 mm.

For identical or similar diameters of threads used, the angles thusdefined make it possible to structurally define the internal layer ofthe cord and the internal strands of this layer in order to obtain acord according to the invention that is easy to manufacture on anindustrial scale by altering only the angles of the threads of thelayers. In addition, the pitches p1, p1′, p2, p2′ and p3, p3′ withinthese preferred ranges make it possible to obtain a cord that exhibitsmechanical properties compatible with tyre use, a relatively low costand a relatively low linear cord weight.

Very Low Modulus Cords of the Invention

In one embodiment, the cord has a very low modulus, namely 50 GPa≤EC≤89GPa. In this embodiment, the ability of the cord to hug the obstaclesencountered is favoured over the ability of the cord to provide the tyrewith high steering capability.

In preferred variants of very low modulus cords, 25 GPa≤EI≤180 GPa,preferably 36 GPa≤EI≤175 GPa. In that particular variant, 25 GPa≤EI≤175GPa.

In a first variant in which the internal layer of the cord with a verylow modulus has a relatively low modulus, 25 GPa≤EI 94 GPa, preferably36 GPa≤EI≤94 GPa. In that particular variant, 25 GPa≤EI≤102 GPa. Asexplained above, the breaking strength of the cord is maximized here byusing a relatively low modulus for the internal layer.

In a second variant in which the internal layer of the cord with a verylow modulus has a higher modulus, 95 GPa≤EI≤180 GPa, preferably 95GPa≤EI≤175 GPa. In that particular variant, 103 GPa≤EI≤175 GPa. Becauseof the very low modulus of the cord, a relatively high value for themodulus of the internal layer entails a relatively low value for themodulus of the external layer therefore leading to excellent resistanceof the cord to cutting.

In an embodiment in which the internal layer of the cord and the cordwith a very low modulus have relatively similar modulus values,0.60≤EC/EI≤1.20. In this variant, the inventors are postulating thehypothesis that the core and the layer work more or less together whenthe cord with a very low modulus is stressed, notably in tension. Inthis way, the compromise between the breaking strength of the cord andits resistance to cutting is maximized.

In an embodiment in which the internal and external layers of the cordwith a very low modulus have relatively different modulus values,EC/EI≤0.59 or 1.21≤EC/EI.

In a variant, the internal layer of the cord with a very low modulus hasa relatively high modulus with respect to the modulus of the externallayer of the cord with a very low modulus, namely EC/EI≤0.59, preferably0.40≤EC/EI≤0.59. This variant favours the resistance of the cord tocutting over its breaking strength.

In another variant, the internal layer of the cord with a very lowmodulus has a relatively low modulus with respect to the modulus of theexternal layer of the cord with a very low modulus, namely 1.21≤EC/EI,preferably 1.21≤EC/EI≤3.00. This variant favours the breaking strengthof the cord over its resistance to cutting.

In preferred variants of the invention, the cords with a very lowmodulus have the following advantageous structural characteristics.

In preferred variants of the invention, the cords with a very lowmodulus have the following advantageous structural characteristics.

In one preferred embodiment, the helix angle α of each internal strandin the internal layer of the cord ranges:

-   -   from 3° to 42° in an embodiment using internal strands and        external strands having two layers,    -   from 6° to 41° in an embodiment using internal strands and        external strands having three layers,    -   from 5° to 36° in an embodiment using internal strands having        two layers and external strands having three layers,    -   from 4° to 36° in an embodiment using internal strands having        three layers and external strands having two layers.

In that particular variant, the helix angle α of each internal strand inthe internal layer of the cord ranges from 9° to 42°.

In one preferred embodiment, the helix angle α′ of each external strandin the external layer of the cord ranges:

-   -   from 13° to 38° in an embodiment using internal strands and        external strands having two layers,    -   from 18° to 36° in an embodiment using internal strands and        external strands having three layers,    -   from 14° to 34° in an embodiment using internal strands having        two layers and external strands having three layers,    -   from 13° to 32° in an embodiment using internal strands having        three layers and external strands having two layers.

In that particular variant, the helix angle α of each internal strand inthe internal layer of the cord ranges from 13° to 32°.

In the particular variant using internal strands having two layers,29°≤2α+β+γ≤136°.

In the particular variant using internal strands having three layers,50°≤3α+β+δ+γ≤80°.

In the particular variant using external strands having two layers,42°≤2α′+β′+γ′≤90°.

In the particular variant using external strands having three layers,65°≤3α′+β′+δ′+γ′≤95°.

In the embodiment using internal strands and external strands having twolayers, 16°≤2α+β+γ≤110°, and

-   -   in an embodiment in which Q=1, advantageously 16°≤2α+β+γ≤74°,        and    -   in an embodiment in which Q>1, advantageously 23°≤2α+β+γ≤110°.

In an embodiment using internal strands and external strands havingthree layers, 29°≤3α+β+δ+γ≤158°, and

-   -   in an embodiment in which Q=1, advantageously 29°≤3α+β+δ+γ≤140°,        and    -   in an embodiment in which Q>1, advantageously 42°≤3α+β+δ+γ≤158°.

In an embodiment using internal strands having two layers and externalstrands having three layers, 20°≤2α+β+γ≤105°, and

-   -   in an embodiment in which Q=1, advantageously 20°≤2α+β+γ≤86°,        and    -   in an embodiment in which Q>1, advantageously 27°≤2α+β+γ≤105°.

In an embodiment using internal strands having three layers and externalstrands having two layers, 35°≤3α+β+δ+γ≤162°, and

-   -   in an embodiment in which Q=1, advantageously 35°≤3α+β+δ+γ≤140°,        and    -   in an embodiment in which Q>1, advantageously 36°≤3α+β+δ+γ≤162°.

In the embodiment using internal strands and external strands having twolayers, 43°≤2α′+β′+γ′≤97°, and

-   -   in an embodiment in which Q′=1, advantageously        47°≤2α′+β′+γ′≤85°, and    -   in an embodiment in which Q′>1, advantageously        43°≤2α′+β′+γ′≤97°.

In an embodiment using internal strands and external strands havingthree layers, 65°≤3α′+β′+δ′+γ′≤153°, and

-   -   in an embodiment in which Q′=1, advantageously        65°≤3α′+β′+δ′+γ′≤143°, and    -   in an embodiment in which Q′>1, advantageously        78°≤3α′+β′+δ′+γ′≤153°.

In an embodiment using internal strands having two layers and externalstrands having three layers, 66°≤3α′+β′+δ′+γ′≤147°, and

-   -   in an embodiment in which Q′=1, advantageously        66°≤3α′+β′+δ′+γ′≤147°, and    -   in an embodiment in which Q′>1, advantageously 75°        53α′+β′+δ′+γ′≤140°.

In an embodiment using internal strands having three layers and externalstrands having two layers, 34°≤2α′+β′+γ′≤96°, and

-   -   in an embodiment in which Q′=1, advantageously        34°≤2α′+β′+γ′≤86°, and    -   in an embodiment in which Q′>1, advantageously        42°≤2α′+β′+γ′≤96°.

In an embodiment using internal strands and external strands having twolayers, 85°≤2α+β+γ+2α′+β′+γ′≤184°. In an embodiment in which Q=1 andQ′=1, advantageously 85°≤2α+β+γ+2α′+β′+γ′≤145°. In an embodiment inwhich Q>1 and Q′=1, advantageously 108°≤2α+β+γ+2α′+β′+γ′≤154°. In anembodiment in which Q=1 and Q′>1, advantageously90°≤2α+β+γ+2α′+β′+γ′≤151°. In an embodiment in which Q>1 and Q′>1,advantageously 110°≤2α+β+γ+2α′+β′+γ′≤184°. In that particular variant,109°≤2α+β+γ+2α′+β′+γ′≤195°.

In an embodiment using internal strands and external strands havingthree layers, 138°≤3α+β+γ+γ+3α′+β′+δ′+γ′≤280°. In an embodiment in whichQ=1 and Q′=1, advantageously 138°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤246°. In anembodiment in which Q>1 and Q′=1, advantageously144°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤261°. In an embodiment in which Q=1 and Q′>1,advantageously 148°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤254°. In an embodiment inwhich Q>1 and Q′>1, advantageously 144°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤280°. Inthat particular variant, 130°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤170°.

In an embodiment using internal strands having two layers and externalstrands having three layers, 146°≤2α+β+γ+3α′+β′+δ′+γ′≤226°. In anembodiment in which Q=1 and Q′=1, advantageously134°≤2α+β+γ+3α′+β′+δ′+γ′≤199°. In an embodiment in which Q>1 and Q′=1,advantageously 130°≤2α+β+γ+3α′+β′+δ′+γ′≤206°. In an embodiment in whichQ=1 and Q′>1, advantageously 152°≤2α+β+γ+3α′+β′+δ′+γ′≤214°. In anembodiment in which Q>1 and Q′>1, advantageously146°≤2α+β+γ+3α′+β′+γ′+γ′≤226°. In that particular variant,110°≤2α+β+γ+3α′+β′+δ′+γ′≤150°.

In an embodiment using internal strands having three layers and externalstrands having two layers, 100°≤3α+β+δ+γ+2α′+β′+γ′≤224°. In anembodiment in which Q=1 and Q′=1, advantageously100°≤3α+β+δ+γ+2α′+β′+γ′≤200°. In an embodiment in which Q>1 and Q′=1,advantageously 104°≤3α+β+δ+γ+2α′+β′+γ′≤212°. In an embodiment in whichQ=1 and Q′>1, advantageously 117°≤3α+β+δ+γ+2α′+β′+γ′≤220°. In anembodiment in which Q>1 and Q′>1, advantageously121°≤3α+β+δ+γ+2α′+β′+γ′≤224°. In that particular variant,110°≤3α+β+δ+γ+2α′+β′+γ′≤150°.

For identical or similar diameters of threads used, the angles thusdefined make it possible to structurally define the internal layer ofthe cord and the internal strands of this layer in order to obtain acord according to the invention that is easy to manufacture on anindustrial scale by altering only the angles of the threads of thelayers. In addition, the pitches p1, p1′, p2, p2′ and p3, p3′ withinthese preferred ranges make it possible to obtain a cord that exhibitsmechanical properties compatible with tyre use, a relatively low costand a relatively low linear cord weight.

The values for the helix angles β, γ, δ, β′, γ′, δ′ and those for thepitches p1, p2, p3, p1′, p2′, p3′ that make it possible to obtain cordswith a very low modulus are identical to those already describedhereinabove.

Low Modulus Cords of the Invention

In another embodiment, the cord has a low modulus, namely 90 GPa≤EC≤130GPa.

In this embodiment, a balanced compromise between the ability of thecord to hug the obstacles encountered and the ability of the cord toprovide the tyre with high steering capability is adopted.

In preferred variants of low modulus cords, 25 GPa≤EI≤180 GPa,preferably 64 GPa≤EI≤180 GPa. In the preferred variant, 35 GPa≤EI≤175GPa.

In a first variant in which the internal layer of the cord with a lowmodulus has a relatively low modulus, 25 GPa≤EI≤94 GPa, preferably 64GPa≤EI≤94 GPa. In that particular variant, 35 GPa≤EI≤102 GPa. Asexplained above, the breaking strength of the cord is maximized here byusing a relatively low modulus for the internal layer.

In a second variant in which the internal layer of the cord with a lowmodulus has a higher modulus, 95 GPa≤EI≤180 GPa. In that particularvariant, 103 GPa≤EI≤175 GPa.

In an embodiment in which the internal layer of the cord and the cordwith a low modulus have relatively similar modulus values,0.60≤EC/EI≤1.20. In this variant, the inventors are postulating thehypothesis that the core and the layer work more or less together whenthe cord with a low modulus is stressed, notably in tension. In thisway, the compromise between the breaking strength of the cord and itsresistance to cutting is maximized.

In an embodiment in which the internal and external layers of the cordwith a low modulus have relatively different modulus values, EC/EI≤0.59or 1.21≤EC/EI.

In a variant, the internal layer of the cord with a low modulus has arelatively high modulus with respect to the modulus of the externallayer of the cord with a low modulus, namely EC/EI≤0.59, preferably0.40≤EC/EI≤0.59. This variant favours the resistance of the cord tocutting over its breaking strength.

In another variant, the internal layer of the cord with a low modulushas a relatively low modulus with respect to the modulus of the externallayer of the cord with a low modulus, namely 1.21≤EC/EI, preferably1.21≤EC/EI≤2.82. This variant favours the breaking strength of the cordover its resistance to cutting.

In preferred variants of the invention, the cords with a very lowmodulus have the following advantageous structural characteristics.

In one preferred embodiment, the helix angle α of each internal strandin the internal layer of the cord ranges:

-   -   from 3° to 36° in an embodiment using internal strands and        external strands having two layers,    -   from 4° to 31° in an embodiment using internal strands and        external strands having three layers,    -   from 3° to 31° in an embodiment using internal strands having        two layers and external strands having three layers,    -   from 4° to 27° in an embodiment using internal strands having        three layers and external strands having two layers.

In that particular variant, the helix angle α of each internal strand inthe internal layer of the cord ranges from 5° to 36°.

In one preferred embodiment, the helix angle α′ of each external strandin the external layer of the cord ranges:

-   -   from 9° to 27° in an embodiment using internal strands and        external strands having two layers,    -   from 13° to 32° in an embodiment using internal strands and        external strands having three layers,    -   from 10° to 31° in an embodiment using internal strands having        two layers and external strands having three layers,    -   from 11° to 31° in an embodiment using internal strands having        three layers and external strands having two layers.

In that particular variant, the helix angle α of each internal strand inthe internal layer of the cord ranges from 10° to 25°.

In the particular variant using internal strands having two layers,27°≤2α+β+γ≤108°.

In the particular variant using internal strands having three layers,50°≤3α+β+γ+γ≤80°.

In the particular variant using external strands having two layers,39°≤2α′+β′+γ′≤65°.

In the particular variant using external strands having three layers,65°≤3α′+β′+δ′+γ′≤95°.

In the embodiment using internal strands and external strands having twolayers, 13°≤2α+β+γ≤110°, and

-   -   in an embodiment in which Q=1, advantageously 13°≤2α+β+γ≤74°,        and    -   in an embodiment in which Q>1, advantageously 16°≤2α+β+γ≤110°.

In an embodiment using internal strands and external strands havingthree layers, 25°≤3α+β+δ+γ≤125°, and

-   -   in an embodiment in which Q=1, advantageously 25°≤3α+β+δ+γ≤120°,        and    -   in an embodiment in which Q>1, advantageously 36°≤3α+β+δ+γ≤125°.

In an embodiment using internal strands having two layers and externalstrands having three layers, 16°≤2α+β+γ≤86°, and

-   -   in an embodiment in which Q=1, advantageously 16°≤2α+β+γ≤86°,        and    -   in an embodiment in which Q>1, advantageously 19°≤2α+β+γ≤85°.

In an embodiment using internal strands having three layers and externalstrands having two layers, 26°≤3α+β+δ+γ≤128°, and

-   -   in an embodiment in which Q=1, advantageously 26°≤3α+β+δ+γ≤113°,        and    -   in an embodiment in which Q>1, advantageously 36°≤3α+β+δ+γS        128°.

In the embodiment using internal strands and external strands having twolayers, 31°≤2α′+β′+γ′≤71°, and

-   -   in an embodiment in which Q′=1, advantageously        31°≤2α′+β′+γ′≤66°, and    -   in an embodiment in which Q′>1, advantageously        39°≤2α′+β′+γ′≤71°.

In an embodiment using internal strands and external strands havingthree layers, 54°≤3α′+β′+δ′+Y's 123°, and

-   -   in an embodiment in which Q′=1, advantageously        54°≤3α′+β′+δ′+γ′≤118°, and    -   in an embodiment in which Q′>1, advantageously        65°≤3α′+β′+δ′+γ′≤123°.

In an embodiment using internal strands having two layers and externalstrands having three layers, 54°≤3α′+β′+δ′+γ′≤125°, and

-   -   in an embodiment in which Q′=1, advantageously        54°≤3α′+β′+δ′+γ′≤120°, and    -   in an embodiment in which Q′>1, advantageously        64°≤3α′+β′+δ′+γ′≤125°.

In an embodiment using internal strands having three layers and externalstrands having two layers, 28°≤2α′+β′+γ′≤89°, and

-   -   in an embodiment in which Q′=1, advantageously        28°≤2α′+β′+γ′≤85°, and    -   in an embodiment in which Q′>1, advantageously        36°≤2α′+β′+γ′≤89°.

In an embodiment using internal strands and external strands having twolayers, 65°≤2α+β+γ+2α′+β′+γ′≤153°. In an embodiment in which Q=1 andQ′=1, advantageously 65°≤2α+β+γ+2α′+β′+γ′≤117°. In an embodiment inwhich Q>1 and Q′=1, advantageously 72°≤2α+β+γ+2α′+β′+γ′≤133°. In anembodiment in which Q=1 and Q′>1, advantageously81°≤2α+β+γ+2α′+β′+γ′≤130°. In an embodiment in which Q>1 and Q′>1,advantageously 79°≤2α+β+γ+2α′+β′+γ′≤153°. In that particular variant,82°≤2α+β+γ+2α′+β′+γ′≤153°.

In an embodiment using internal strands and external strands havingthree layers, 107°≤3α+β+γ+γ+3α′+β′+δ′+γ′≤211°. In an embodiment in whichQ=1 and Q′=1, advantageously 107°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤197°. In anembodiment in which Q>1 and Q′=1, advantageously113°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤206°. In an embodiment in which Q=1 and Q′>1,advantageously 115°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤202°. In an embodiment inwhich Q>1 and Q′>1, advantageously 120°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤211°. Inthat particular variant, 130°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤170°.

In an embodiment using internal strands having two layers and externalstrands having three layers, 87°≤2α+β+γ+3α′+β′+δ′+γ′≤172°. In anembodiment in which Q=1 and Q′=1, advantageously87°≤2α+β+γ+3α′+β′+δ′+γ′≤160°. In an embodiment in which Q>1 and Q′=1,advantageously 90°≤2α+β+γ+3α′+β′+δ′+γ′≤165°. In an embodiment in whichQ=1 and Q′>1, advantageously 111°≤2α+β+γ+3α′+β′+δ′+γ′≤166°. In anembodiment in which Q>1 and Q′>1, advantageously111°≤2α+β+γ+3α′+β′+δ′+γ′≤172°. In that particular variant,110°≤2α+β+γ+3α′+β′+δ′+γ′≤150°.

In an embodiment using internal strands having three layers and externalstrands having two layers, 74°≤3α+β+δ+γ+2α′+β′+γ′≤183°. In an embodimentin which Q=1 and Q′=1, advantageously 74°≤3α+β+δ+γ+2α′+β′+γ′≤158°. In anembodiment in which Q>1 and Q′=1, advantageously86°≤3α+β+δ+γ+2α′+β′+γ′≤168°. In an embodiment in which Q=1 and Q′>1,advantageously 84°≤3α+β+δ+γ+2α′+β′+γ′≤168°. In an embodiment in whichQ>1 and Q′>1, advantageously 94°≤3α+β+δ+γ+2α′+β′+γ′≤183°. In thatparticular variant, 110°≤3α+β+δ+γ+2α′+β′+γ′≤150°.

For identical or similar diameters of threads used, the angles thusdefined make it possible to structurally define the internal layer ofthe cord and the internal strands of this layer in order to obtain acord according to the invention that is easy to manufacture on anindustrial scale by altering only the angles of the threads of thelayers. In addition, the pitches p1, p1′, p2, p2′ and p3, p3′ withinthese preferred ranges make it possible to obtain a cord that exhibitsmechanical properties compatible with tyre use, a relatively low costand a relatively low linear cord weight.

The values for the helix angles β, γ, δ, β′, γ′, δ′ and those for thepitches p1, p2, p3, p1′, p2′, p3′ that make it possible to obtain cordswith a low modulus are identical to those already described hereinabove.

Medium Modulus Cords of the Invention

In yet another embodiment, the cord has a medium modulus, namely 131GPa≤EC≤160 GPa. In this embodiment, the ability of the cord to providethe tyre with high steering capability is favoured over the ability ofthe cord to hug the obstacles encountered.

In preferred variants of medium modulus cords, 78 GPa≤EI≤180 GPa,preferably 100 GPa≤EI≤180 GPa. In that preferred variant, 125 GPa≤EI≤180GPa.

In a first variant in which the internal layer of the cord with a mediummodulus has a relatively low modulus, 78 GPa≤EI≤94 GPa. As explainedabove, the breaking strength of the cord is maximized here by using arelatively low modulus for the internal layer.

In a second variant in which the internal layer of the cord with a lowmodulus has a higher modulus, 95 GPa≤EI≤180 GPa.

In an embodiment in which the internal layer of the cord and the cordwith a medium modulus have relatively similar modulus values,0.60≤EC/EI≤1.20, preferably 0.80≤EC/EI≤1.15. In this embodiment, theinventors are postulating the hypothesis that the core and the layerwork more or less together when the cord with a medium modulus isstressed, notably in tension. In this way, the compromise between thebreaking strength of the cord and its resistance to cutting ismaximized.

In an embodiment in which the internal and external layers of the cordwith a medium modulus have relatively different modulus values,EC/EI≤0.59 or 1.21≤EC/EI.

In a variant, the internal layer of the cord with a medium modulus has arelatively high modulus with respect to the modulus of the externallayer of the cord with a medium modulus, namely EC/EI≤0.59, preferably0.40≤EC/EI≤0.59. This variant favours the resistance of the cord tocutting over its breaking strength.

In another variant, the internal layer of the cord with a medium modulushas a relatively low modulus with respect to the modulus of the externallayer of the cord with a medium modulus, namely 1.21≤EC/EI, preferably1.21≤EC/EI≤3.00. This variant favours the breaking strength of the cordover its resistance to cutting.

In preferred variants of the invention, the cords with a medium modulushave the following advantageous structural characteristics.

In one preferred embodiment, the helix angle α of each internal strandin the internal layer of the cord ranges:

-   -   from 3° to 24° in an embodiment using internal strands and        external strands having two layers,    -   from 4° to 22° in an embodiment using internal strands and        external strands having three layers,    -   from 3° to 20° in an embodiment using internal strands having        two layers and external strands having three layers,    -   from 4° to 23° in an embodiment using internal strands having        three layers and external strands having two layers.

In that particular variant, the helix angle α of each internal strand inthe internal layer of the cord ranges from 5° to 19°.

In one preferred embodiment, the helix angle α′ of each external strandin the external layer of the cord ranges:

-   -   from 11° to 20° in an embodiment using internal strands and        external strands having two layers,    -   from 11° to 21° in an embodiment using internal strands and        external strands having three layers,    -   from 10° to 22° in an embodiment using internal strands having        two layers and external strands having three layers,    -   from 10° to 27° in an embodiment using internal strands having        three layers and external strands having two layers.

In that particular variant, the helix angle α′ of each external strandin the external layer of the cord ranges from 11° to 20°.

In the particular variant using internal strands having two layers,23°≤2α+β+γ≤55°.

In the particular variant using internal strands having three layers,50°≤3α+β+δ+γ≤80°.

In the particular variant using external strands having two layers,39°≤2α′+β′+γ′≤57°.

In the particular variant using external strands having three layers,65°≤3α′+β′+δ′+γ′≤95°.

In the embodiment using internal strands and external strands having twolayers. 11°≤2α+3+γ≤64°, and

-   -   in an embodiment in which Q=1, advantageously 110°≤2α+β+γ≤64°,        and    -   in an embodiment in which Q>1, advantageously 16°≤2α+β+γ≤63°.

In an embodiment using internal strands and external strands havingthree layers, 25°≤δ3α+β+γ+δ≤97°, and

-   -   in an embodiment in which Q=1, advantageously 25°≤3α+β+γ+δ≤97°,        and    -   in an embodiment in which Q>1, advantageously 36°≤3α+β+γ+δ≤97°.

In an embodiment using internal strands having two layers and externalstrands having three layers, 16°≤2α+β+γ≤68°, and

-   -   in an embodiment in which Q=1, advantageously 16°≤2α+β+γ≤56°,        and    -   in an embodiment in which Q>1, advantageously 20°≤2α+β+γ≤68°.

In an embodiment using internal strands having three layers and externalstrands having two layers, 26°≤3α+β+γ+δ≤97°, and

-   -   in an embodiment in which Q=1, advantageously 26°≤3α+β+γ+δ≤86°,        and    -   in an embodiment in which Q>1, advantageously 36°≤3α+β+γ+δ≤97°.

In the embodiment using internal strands and external strands having twolayers, 23°≤2α′+β′+γ′≤58°, and

-   -   in an embodiment in which Q′=1, advantageously        23°≤2α′+β′+γ′≤52°, and    -   in an embodiment in which Q′>1, advantageously        27°≤2α′+β′+γ′≤58°.

In an embodiment using internal strands and external strands havingthree layers, 48° 53α′+β′+γ′+δ's 89°, and

-   -   in an embodiment in which Q′=1, advantageously        48°≤3α′+β′+γ′+δ′+δ′≤81°, and    -   in an embodiment in which Q′>1, advantageously        61°≤3α′+β′+γ′+δ′≤89°.

In an embodiment using internal strands having two layers and externalstrands having three layers, 47°≤3α′+β′+γ′+δ′≤89°, and

-   -   in an embodiment in which Q′=1, advantageously        47°≤3α′+β′+γ′+δ′≤86°, and    -   in an embodiment in which Q′>1, advantageously        62°≤3α′+β′+γ′+δ′≤89°.

In an embodiment using internal strands having three layers and externalstrands having two layers, 30°≤2α′+β′+γ′≤64° and

-   -   in an embodiment in which Q′=1, advantageously        30°≤2α′+β′+γ′≤62°, and    -   in an embodiment in which Q′>1, advantageously        37°≤2α′+β′+γ′≤64°.

In an embodiment using internal strands and external strands having twolayers, 45°≤2α+β+γ+2α′+β′+γ′≤108°. In an embodiment in which Q=1 andQ′=1, advantageously 45°≤2α+β+γ+2α′+β′+γ′≤95°. In an embodiment in whichQ>1 and Q′=1, advantageously 55°≤2α+β+γ+2α′+β′+γ′≤95°. In an embodimentin which Q=1 and Q′>1, advantageously 56°≤2α+β+γ+2α′+β′+γ′≤102°. In anembodiment in which Q>1 and Q′>1, advantageously60°≤2α+β+γ+2α′+β′+γ′≤108°. In that particular variant,73°≤2α+β+γ+2α′+β′+γ′≤102°.

In an embodiment using internal strands and external strands havingthree layers, 84°≤3α+β+γ+δ+3α′+β′+γ′+δ′≤161°. In an embodiment in whichQ=1 and Q′=1, advantageously 84°≤3α+β+γ+1+3α′+β′+γ′+δ′≤153°. In anembodiment in which Q>1 and Q′=1, advantageously94°=3α+β+γ+δ+3α′+β′+γ′+δ′≤151°. In an embodiment in which Q=1 and Q′>1,advantageously 88°≤3α+β+γ+δ+3α′+β′+γ′+δ′≤153°. In an embodiment in whichQ>1 and Q′>1, advantageously 101°≤3α+β+γ+δ+3α′+β′+γ′+δ′≤161°. In thatparticular variant, 130°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤170°.

In an embodiment using internal strands having two layers and externalstrands having three layers, 84°≤2α+β+γ+3α′+β′+γ′+δ′≤136°. In anembodiment in which Q=1 and Q′=1, advantageously84°≤2α+β+γ+3α′+β′+γ′+δ′≤112°. In an embodiment in which Q>1 and Q′=1,advantageously 88°≤2α+β+γ+3α′+β′+γ′+δ′≤124°. In an embodiment in whichQ=1 and Q′>1, advantageously 96°≤2α+β+γ+3α′+β′+γ′+δ′≤122°. In anembodiment in which Q>1 and Q′>1, advantageously99°≤2α+β+γ+3α′+β′+γ′+δ′≤136°. In that particular variant,110°≤2α+β+γ+3α′+β′+δ′+γ′≤150°.

In an embodiment using internal strands having three layers and externalstrands having two layers, 64°≤3α+β+γ+δ+2α′+β′+γ′≤135°. In an embodimentin which Q=1 and Q′=1, advantageously 64°≤3α+β+γ+δ+2α′+β′+γ′≤117°. In anembodiment in which Q>1 and Q′=1, advantageously73°≤3α+β+γ+δ+2α′+β′+γ′≤131°. In an embodiment in which Q=1 and Q′>1,advantageously 68°≤3α+β+γ+δ+2α′+β′+γ′≤127°. In an embodiment in whichQ>1 and Q′>1, advantageously 80°≤3α+β+γ+δ+2α′+β′+γ′≤135°. In thatparticular variant, 110°≤3α+β+γ+γ+2α′+β′+γ′≤150°.

For identical or similar diameters of threads used, the angles thusdefined make it possible to structurally define the internal layer ofthe cord and the internal strands of this layer in order to obtain acord according to the invention that is easy to manufacture on anindustrial scale by altering only the angles of the threads of thelayers. In addition, the pitches p1, p1′, p2, p2′ and p3, p3′ withinthese preferred ranges make it possible to obtain a cord that exhibitsmechanical properties compatible with tyre use, a relatively low costand a relatively low linear cord weight.

The values for the helix angles β, γ, δ, β′, γ′, δ′ and those for thepitches p1, p2, p3, p1′, p2′, p3′ that make it possible to obtain cordswith a medium modulus are identical to those already describedhereinabove.

Architecture of the Cords According to the Invention

Advantageously, J=2, 3 or 4, preferably J=3 or 4.

In one embodiment, L is equal to 7, 8, 9 or 10, preferably L=8, 9 or 10and more preferentially L=8 or 9.

In a first variant, J=2 and L=7 or 8, preferably J=2, L=7.

In a second variant, J=3 and L=7, 8 or 9, preferably J=3, L=8 or 9.Instances in which L=8 favour the desaturation of the external layer ofthe cord and therefore the penetrability of the cord between theexternal strands. Instances in which L=9 maximize the number of externalstrands and therefore the breaking strength of the cord.

In a third variant, J=4 and L=7, 8, 9 or 10, preferably J=4, L=9.

In these embodiments, notably those in which J=3 or 4, there is a riskof seeing a significant spread of corrosive agents between the J=3 or 4internal strands which delimit a central capillary which very muchencourages them to spread along the cord, when the cord isinsufficiently penetrated. This disadvantage can be overcome byrendering the cord capable of being penetrated by the elastomer compoundwhich then prevents the corrosive agents from accessing the centralcapillary and, in the best of cases in which the central capillary isitself penetrated, prevents these corrosive agents from spreading alongthe cord.

Advantageously, the external layer of the cord is desaturated.

By definition, a desaturated layer of strands is such that there isenough space between the strands to allow an elastomer compound to pass.An external layer of strands is desaturated means that the externalstrands do not touch and that there is enough space between two adjacentexternal strands to allow an elastomer compound to pass as far as theinternal strands. By contrast, a saturated layer of strands is such thatthere is not enough space between the strands of the layer to allow anelastomer compound to pass, for example because each pair of two strandsof the layer touch one another.

Advantageously, the inter-strand distance of the external layer ofexternal strands, defined, on a cross section of the cord perpendicularto the main axis of the cord, as being the shortest distance separating,on average, the circular envelopes in which two adjacent externalstrands are inscribed, is, for a desaturated layer of strands, greaterthan or equal to 30 μm. For preference, the mean inter-strand distanceseparating two adjacent external strands is greater than or equal to 70μm, more preferentially than/to 100 μm, more preferentially stillthan/to 150 μm, and highly preferentially than/to 200 μm.

As already explained hereinabove, as the cords according to theinvention have an architecture in which J>1, the most severe transverseloadings applied to the cord when the latter is tensioned are thetransverse loadings applied between the internal strands, unlike a cordin which J=1 and in which the most severe transverse loadings are thetransverse loadings applied by the external strands to the internalstrands. Cords exhibiting an architecture in which J>1 and comprising anumber of external strands such that the external layer of the cord issaturated so as to maximize the breaking strength by adding a maximumnumber of external strands are known from the prior art. Here, thanks tothe fact that the external layer of the cord is desaturated, the cordhas, on the one hand, spaces between the external strands that allow theelastomer compound to pass, therefore allowing the cord to be renderedless sensitive to corrosion. On the other hand, although the number ofexternal strands is reduced, the desaturation of the external layer ofthe cord allows the elastomer compound to penetrate, on the one hand,between the external strands and, on the other hand, between theinternal strands so as to form a cushion of elastomer compound that atleast partially absorbs the transverse loadings applied between theinternal strands. Thus, by comparison with a similar cord having asaturated external layer of the cord, the breaking strength obtained isequivalent and the resistance to corrosion is greatly improved.

In an embodiment that promotes the penetrability of the cord, theexternal layer of the cord is incompletely unsaturated.

By definition, a completely unsaturated layer of strands is, as opposedto an incompletely unsaturated layer, such that there is sufficientspace in this layer to add in at least one (X+1)th strand having thesame diameter as the X strands of the layer, it thus being possible fora plurality of strands to be, or to not be, in contact with one another.In this particular instance, there is enough space in the external layerof the cord to add in at least one (L+1)th strand having the samediameter as the L external strands of the external layer of the cord.

Thus, advantageously, the sum SIE of the inter-strand distances E of theexternal layer of the cord is such that SIE≥DE. The sum SIE is the sumof the inter-strand distances E separating each pair of adjacent strandsof the layer. The inter-strand distance of a layer is defined, in asection of the cord perpendicular to the main axis of the cord, as beingthe shortest distance, which, on average, separates two adjacent strandsof the layer. Thus, the inter-strand distance E is calculated bydividing the sum SIE by the number of spaces separating the strands ofthe layer.

In another embodiment that promotes the compromise between penetrabilityand breaking strength, the external layer of the cord is incompletelyunsaturated.

A layer that is incompletely unsaturated with strands is such that thereis not enough space in this layer to add in at least one (X+1)th strandhaving the same diameter as the X strands of the layer. In thisparticular instance, there is not enough space in the external layer toadd in at least one (L+1)th external strand having the same diameter asthe L external strands of the external layer of the cord.

By definition, the diameter of the internal layer DI is the diameter ofthe smallest circle inside which the internal strands are circumscribed.The diameter of an external strand DE is the diameter of the smallestcircle inside which the external strand is circumscribed. For relativelyhigh values of DI/DE, the passage of the elastomer compound between theexternal strands is further promoted, and, for relatively low values ofDI/DE, the architectural stability of the cord is ensured, the breakingstrength is maximized while at the same time allowing the elastomercompound to pass between the external strands, the external diameter ofthe cord is limited, and the thickness of the ply is reduced, astherefore are the heating, rolling resistance and mass of the tyre.

Internal Strands of the Cords According to the Invention

Two-Layer Internal Strands

In one embodiment which favours the compromise between the diameter ofthe cord and the breaking strength, each internal strand has two layersand comprises:

-   -   an internal layer made up of Q≥1 internal threads, and    -   an external layer made up of N>1 external threads wound around        the internal layer.

Each internal strand has two layers, which means to say that itcomprises an assembly made up of two layers of threads, neither more norless, which means to say that the assembly has two layers of threads,not one, not three, but only two. The external layer of each strand iswound around the internal layer of this strand in contact with theinternal layer of this strand.

In one embodiment, D1 and D2 each range from 0.15 mm to 0.60 mm,preferably from 0.20 mm to 0.50 mm, more preferentially from 0.23 mm to0.45 mm, and even more preferentially from 0.25 mm to 0.40 mm.

In preferred embodiments, Q=1, 2, 3 or 4.

In one embodiment, Q=1, N=5 or 6, preferably Q=1, N=6.

In preferred embodiments that make it possible to increase the breakingstrength of the cord with respect to the embodiment in which Q=1, Q=2, 3or 4, preferably Q=3 or 4.

In these preferred embodiments in which Q>1, notably those in which Q=3or 4, there is a risk, when the strand is insufficiently penetrated, ofseeing a significant spread of corrosive agents between the Q=3 or 4internal threads which delimit a central capillary which very muchencourages them to spread along each strand. This disadvantage can beovercome by rendering the strand capable of being penetrated by theelastomer compound which then prevents the corrosive agents fromaccessing the central capillary and, in the best of cases in which thecentral capillary is itself penetrated, prevents these corrosive agentsfrom spreading along the strand.

In preferred embodiments in which Q>1, N=7, 8, 9 or 10, preferably N=8,9 or 10 and more preferentially N=8 or 9.

In a first variant, Q=2 and N=7 or 8, preferably Q=2, N=7.

In a second variant, Q=3 and N=7, 8 or 9, preferably Q=3, N=8.

In a third variant, Q=4 and N=7, 8, 9 or 10, preferably Q=4, N=9.

Advantageously, the external layer of each internal strand isdesaturated, preferably completely unsaturated.

By definition, a desaturated layer of threads is such that there isenough space between the threads to allow an elastomer compound to pass.Thus, a layer that is desaturated means that the threads of this layerdo not touch and that there is enough space between two adjacent threadsof the layer to allow an elastomer compound to pass through the layer.By contrast, a saturated layer of threads is such that there is notenough space between the threads of the layer to allow an elastomercompound to pass, for example because each pair of two threads of thelayer touch one another.

Advantageously, the inter-thread distance of the external layer of eachinternal strand is greater than or equal to 5 μm. For preference, theinter-thread distance of the external layer of each internal strand isgreater than or equal to 15 μm, more preferentially greater than orequal to 35 μm, more preferentially still greater than or equal to 50 μmand highly preferentially greater than or equal to 60 μm.

The fact that the external layer of the internal strand is desaturatedadvantageously makes it easier for the elastomer compound to pass as faras the centre of the internal strand, and thus render the internalstrand less sensitive to corrosion.

By definition, a completely unsaturated layer of threads is such thatthere is sufficient space in this layer to add in at least one (X+1)ththread having the same diameter as the X threads of the layer, it thusbeing possible for a plurality of threads to be in contact, or not incontact, with one another. In this particular instance, there is enoughspace in the external layer of each internal strand to add in at leastone (N+1)th external thread having the same diameter as the N externalthreads of the external layer.

The fact that the external layer of each internal strand is completelyunsaturated makes it possible to maximise the penetration of theelastomer compound into each internal strand, and thus render eachinternal strand even less sensitive to corrosion.

Thus, advantageously, the sum SI2 of the inter-thread distances of theexternal layer of each internal strand is such that SI2≥D2. The sum SI2is the sum of the inter-thread distances separating each pair ofadjacent threads of the layer. The inter-thread distance of a layer isdefined, in a section of the cord perpendicular to the main axis of thecord, as being the shortest distance which, on average, separates twoadjacent threads of the layer. Thus, the inter-thread distance iscalculated by dividing the sum SI2 by the number of spaces separatingthe threads of the layer.

By contrast, a layer of threads that is incompletely unsaturated wouldbe such that there would not be enough space in this layer to add in atleast one (X+1)th thread having the same diameter as the X′ threads ofthe layer. In this particular instance, there would not be enough spacein the external layer to add in at least one (N+1)th external threadhaving the same diameter as the N external threads of the externallayer.

In preferred embodiments, each internal thread of each internal strandhas a diameter D1 greater than or equal to the diameter D2 of eachexternal thread of each internal strand. The use of diameters such thatD1>D2 makes it possible to promote the penetrability of the elastomercompound through the intermediate layer. The use of diameters such thatD1=D2 makes it possible to limit the number of different threads to bemanaged in the manufacture of the cord.

Advantageously, each internal strand is of the type not rubberized insitu. What is meant by not rubberized in situ is that, prior to theassembly of the internal layer of the cord, and prior to the assembly ofthe cord, each internal strand is made up of the threads of the variouslayers and does not have any polymer compound, notably any elastomercompound.

Advantageously, the internal layer of the cord is wound in a cordinternal-layer direction, and each internal layer (when Q>1) andexternal layer of each internal strand is wound in the same direction ofwinding as the cord internal-layer direction.

Three-Layer Internal Strands

In another particularly advantageous embodiment that improves thebreaking strength of the cord, each internal strand has three layers andcomprises:

-   -   an internal layer made up of Q≥1 internal threads,    -   an intermediate layer made up of P>1 intermediate threads wound        around the internal layer, and    -   an external layer made up of N>1 external threads wound around        the intermediate layer.

Each internal strand has three layers, which means to say that itcomprises an assembly made up of three layers of threads, neither morenor less, which means to say that the assembly has three layers ofthreads, not two, not four, but only three. The external layer of eachstrand is wound in a helix around the intermediate layer of this strandin contact with the intermediate layer of this strand. The intermediatelayer of each strand is wound in a helix around the internal layer ofthis strand in contact with the internal layer of this strand.

In one embodiment, D1, D2 and D3 each range from 0.15 mm to 0.60 mm,preferably from 0.20 mm to 0.50 mm, more preferentially from 0.23 mm to0.45 mm, and even more preferentially from 0.25 mm to 0.40 mm.

In preferred embodiments, Q=1, 2, 3 or 4.

In one embodiment, Q=1, P=5 or 6 and N=10, 11 or 12, preferably Q=1, P=5or 6 and N=10 or 11 and more preferentially Q=1, P=6 and N=11.

In preferred embodiments that make it possible to increase the breakingstrength of the cord with respect to the embodiment in which Q=1, Q=2, 3or 4, preferably Q=3 or 4.

In these preferred embodiments in which Q>1, notably those in which Q=3or 4, there is a risk, when the strand is insufficiently penetrated, ofseeing a significant spread of corrosive agents between the Q=3 or 4internal threads which delimit a central capillary which very muchencourages them to spread along each strand. This disadvantage can beovercome by rendering the strand capable of being penetrated by theelastomer compound which then prevents the corrosive agents fromaccessing the central capillary and, in the best of cases in which thecentral capillary is itself penetrated, prevents these corrosive agentsfrom spreading along the strand.

In preferred embodiments in which Q>1, Q=2, 3 or 4, P=7, 8, 9 or 10,N=13, 14 or 15, preferably Q=3 or 4, P=8, 9 or 10, N=14 or 15, morepreferentially Q=3, P=8 or 9 and N=14 or 15 and more preferentiallystill Q=3, P=9 and N=15.

Advantageously, the intermediate layer of each internal strand isdesaturated.

By definition, a desaturated layer of threads is such that there isenough space between the threads to allow an elastomer compound to pass.Thus, a layer that is desaturated means that the threads of this layerdo not touch and that there is enough space between two adjacent threadsof the layer to allow an elastomer compound to pass through the layer.By contrast, a saturated layer of threads is such that there is notenough space between the threads of the layer to allow an elastomercompound to pass, for example because each pair of two threads of thelayer touch one another.

Advantageously, the inter-thread distance of the intermediate layer ofeach internal strand is greater than or equal to 5 μm. For preference,the inter-thread distance of the intermediate layer of each internalstrand is greater than or equal to 15 μm, more preferentially greaterthan or equal to 35 μm, more preferentially still greater than or equalto 50 μm and highly preferentially greater than or equal to 60 μm.

The fact that the intermediate layer of the internal strand isdesaturated advantageously makes it easier for the elastomer compound topass as far as the centre of each internal strand, and thus render eachinternal strand less sensitive to corrosion.

In an embodiment that promotes the compromise between penetrability ofeach internal strand and breaking strength, the intermediate layer ofeach internal strand is incompletely unsaturated.

By definition, a layer of threads that is incompletely unsaturated issuch that there is not enough space in this layer to add in at least one(X+1)th thread having the same diameter as the X threads of the layer.In this particular instance, there is not enough space in theintermediate layer to add in at least one (P+1)th intermediate threadhaving the same diameter as the P intermediate threads of theintermediate layer.

The fact that the intermediate layer of the internal strand isincompletely unsaturated makes it possible to ensure an architecturalstability of the intermediate layer. Furthermore, the fact that theintermediate layer of the internal strand is incompletely unsaturatedmakes it possible to ensure that the internal strand comprises arelatively high number of intermediate threads and therefore exhibits arelatively high breaking strength.

Thus, advantageously, the sum SI2 of the inter-thread distances of theintermediate layer is such that SI2<D3 where D3 is the diameter of eachexternal thread of the internal strand, preferably SI2≤0.8×D3. The sumSI2 is the sum of the inter-thread distances separating each pair ofadjacent threads of the intermediate layer. The inter-thread distance ofa layer is defined, in a section of the cord perpendicular to the mainaxis of the cord, as being the shortest distance which, on average,separates two adjacent threads of the layer. Thus, the inter-threaddistance is calculated by dividing the sum SI2 by the number of spacesseparating the threads of the intermediate layer. Because the diameterD3 of the external threads of the external layer of the internal strandis preferentially greater than the sum SI2, the external threads areprevented from penetrating the intermediate layer. This then ensuresgood architectural stability, thereby additionally reducing the risk ofalteration to the radial passage windows for the elastomer compound andtherefore the risk of degrading the good penetrability of the internalstrand.

In another embodiment that promotes the penetrability of each internalstrand, the intermediate layer of each internal strand is completelyunsaturated.

By definition, a completely unsaturated layer of threads is such thatthere is sufficient space in this layer to add in at least one (X+1)ththread having the same diameter as the X threads of the layer, it thusbeing possible for a plurality of threads to be in contact, or not incontact, with one another. In this particular instance, there is enoughspace in the intermediate layer of each internal strand to add in atleast one (P+1)th intermediate thread having the same diameter as the Pintermediate threads of the intermediate layer.

Such an embodiment is particularly advantageous when Q=3 and P=8 or Q=4and P=9 and when D1=D2. Specifically, if we had Q=3 and P=9 or Q=4 andP=10, then the intermediate layer, although desaturated, might, incertain instances, have an inter-thread distance insufficient to ensuresatisfactory penetrability of the strand. Advantageously, the externallayer of each internal strand is desaturated, preferably completelyunsaturated.

As has already been specified, by definition, a desaturated layer ofthreads of threads is such that there is enough space between thethreads to allow an elastomer compound to pass. Thus, a layer that isdesaturated means that the threads of this layer do not touch and thatthere is enough space between two adjacent threads of the layer to allowan elastomer compound to pass through the layer. By contrast, asaturated layer of threads is such that there is not enough spacebetween the threads of the layer to allow an elastomer compound to pass,for example because each pair of two threads of the layer touch oneanother.

Advantageously, the inter-thread distance of the external layer of eachinternal strand is greater than or equal to 5 μm. For preference, theinter-thread distance of the external layer of each internal strand isgreater than or equal to 15 μm, more preferentially greater than orequal to 35 μm, more preferentially still greater than or equal to 50 μmand highly preferentially greater than or equal to 60 μm.

The fact that the external layer of each internal strand is desaturatedadvantageously makes it easier for the elastomer compound to pass as faras the centre of each internal strand, and thus render each internalstrand less sensitive to corrosion.

By definition, a completely unsaturated layer of threads is such thatthere is sufficient space in this layer to add in at least one (X+1)ththread having the same diameter as the X threads of the layer, it thusbeing possible for a plurality of threads to be in contact, or not incontact, with one another. In this particular instance, there is enoughspace in the external layer of each internal strand to add in at leastone (N+1)th external thread having the same diameter as the N externalthreads of the external layer.

The fact that the external layer of each internal strand is completelyunsaturated makes it possible to maximise the penetration of theelastomer compound into each internal strand, and thus render eachinternal strand even less sensitive to corrosion.

Thus, advantageously, the sum SI3 of the inter-thread distances of theexternal layer of each internal strand is such that SI3≥D3. The sum SI3is the sum of the inter-thread distances separating each pair ofadjacent threads of the external layer. The inter-thread distance of alayer is defined, in a section of the cord perpendicular to the mainaxis of the cord, as being the shortest distance which, on average,separates two adjacent threads of the layer. Thus, the inter-threaddistance is calculated by dividing the sum SI3 by the number of spacesseparating the threads of the external layer.

In preferred embodiments, each internal thread of each internal strandhas a diameter D1 greater than or equal to the diameter D2 of eachintermediate thread of each internal strand.

The use of diameters such that D1>D2 makes it possible to promote thepenetrability of the elastomer compound through the intermediate layer.The use of diameters such that D1=D2 makes it possible to limit thenumber of different threads to be managed in the manufacture of thecord.

In preferred embodiments, each internal thread of each internal strandhas a diameter D1 greater than or equal to the diameter D3 of eachexternal thread of each internal strand. The use of diameters such thatD1>D3 makes it possible to promote the penetrability of the elastomercompound through the external layer. The use of diameters such thatD1=D3 makes it possible to limit the number of different threads to bemanaged in the manufacture of the cord.

In preferred embodiments, each intermediate thread of each internalstrand has a diameter D2 equal to the diameter D3 of each externalthread of each internal strand. The use of diameters such that D2=D3makes it possible to limit the number of different threads to be managedin the manufacture of the cord.

Advantageously, each internal strand is of the type not rubberized insitu. What is meant by not rubberized in situ is that, prior to theassembly of the internal layer of the cord, and prior to the assembly ofthe cord, each internal strand is made up of the threads of the variouslayers and does not have any polymer compound, notably any elastomercompound.

Advantageously, the internal layer of the cord is wound in a cordinternal-layer direction, and each internal layer (when Q>1),intermediate layer and external layer of each internal strand is woundin the same direction of winding as the cord internal-layer direction.

External Strands of the Cords According to the Invention

Two-Layer External Strands

In one embodiment which favours the compromise between the diameter ofthe cord and the breaking strength, each external strand has two layersand comprises:

-   -   an internal layer made up of Q′≥1 internal threads,    -   an external layer made up of N′>1 external threads wound around        the internal layer.

Each external strand has two layers, which means to say that itcomprises an assembly made up of two layers of threads, neither more norless, which means to say that the assembly has two layers of threads,not one, not three, but only two. The external layer of each strand iswound around the internal layer of this strand in contact with theinternal layer of this strand.

In one embodiment, D1′ and D2′ each range from 0.15 mm to 0.60 mm,preferably from 0.20 mm to 0.50 mm, more preferentially from 0.23 mm to0.45 mm, and even more preferentially from 0.25 mm to 0.40 mm.

In one embodiment, Q′=1. In this embodiment, N′=5 or 6, preferably N=6.

In preferred embodiments that make it possible to increase the breakingstrength of the cord with respect to the embodiment in which Q′=1, Q=2′,3 or 4, preferably Q′=3 or 4.

In these preferred embodiments in which Q′>1, notably those in whichQ′=3 or 4, there is a risk, when the strand is insufficientlypenetrated, of seeing a significant spread of corrosive agents betweenthe Q′=3 or 4 internal threads which delimit a central capillary whichvery much encourages them to spread along each strand. This disadvantagecan be overcome by rendering the strand capable of being penetrated bythe elastomer compound which then prevents the corrosive agents fromaccessing the central capillary and, in the best of cases in which thecentral capillary is itself penetrated, prevents these corrosive agentsfrom spreading along the strand.

In preferred embodiments in which Q′>1, N′=7, 8, 9 or 10, preferablyN′=8, 9 or 10 and more preferentially N′=8 or 9.

In a first variant, Q′=2 and N′=7 or 8, preferably Q′=2, N′=7.

In a second variant, Q′=3 and N′=7, 8 or 9, preferably Q′=3, N′=8.

In a third variant, Q′=4 and N′=7, 8, 9 or 10, preferably Q′=4, N′=9.

Advantageously, the external layer of each external strand isdesaturated, preferably completely unsaturated.

As has already been specified, by definition, a desaturated layer ofthreads of threads is such that there is enough space between thethreads to allow an elastomer compound to pass. Thus, a layer that isdesaturated means that the threads of this layer do not touch and thatthere is enough space between two adjacent threads of the layer to allowan elastomer compound to pass through the layer. By contrast, asaturated layer of threads is such that there is not enough spacebetween the threads of the layer to allow an elastomer compound to pass,for example because each pair of two threads of the layer touch oneanother.

Advantageously, the inter-thread distance of the external layer of eachexternal strand is greater than or equal to 5 μm. For preference, theinter-thread distance of the external layer of each external strand isgreater than or equal to 15 μm, more preferentially greater than orequal to 35 μm, more preferentially still greater than or equal to 50 μmand highly preferentially greater than or equal to 60 μm.

The fact that the external layer of each external strand is desaturatedadvantageously makes it easier for the elastomer compound to pass as faras the centre of each external strand, and thus render each externalstrand less sensitive to corrosion.

By definition, a completely unsaturated layer of threads is such thatthere is sufficient space in this layer to add in at least one (X′+1)ththread having the same diameter as the X′ threads of the layer, it thusbeing possible for a plurality of threads to be in contact, or not incontact, with one another. In this particular instance, there is enoughspace in the external layer of each external strand to add in at leastone (N′+1)th external thread having the same diameter as the N′ externalthreads of the external layer.

The fact that the external layer of each external strand is completelyunsaturated makes it possible to maximize the penetration of theelastomer compound into each external strand, and thus render eachexternal strand even less sensitive to corrosion.

Thus, advantageously, the sum SI2′ of the inter-thread distances of theexternal layer of each internal strand is such that SI2′ 0 D2′. The sumSI2′ is the sum of the inter-thread distances separating each pair ofadjacent threads of the layer. The inter-thread distance of a layer isdefined, in a section of the cord perpendicular to the main axis of thecord, as being the shortest distance which, on average, separates twoadjacent threads of the layer. Thus, the inter-thread distance iscalculated by dividing the sum SI2′ by the number of spaces separatingthe threads of the layer.

By contrast, a layer that is incompletely unsaturated would be such thatthere would not be enough space in this layer to add in at least one(X′+1)th thread having the same diameter as the X′ threads of the layer.In this particular instance, there would not be enough space in theexternal layer to add in at least one (N′+1)th external thread havingthe same diameter as the N external threads of the external layer.

In preferred embodiments, each internal thread of each external strandhas a diameter D1′ greater than or equal to the diameter D2′ of eachexternal thread of each external strand.

The use of diameters such that D1>D2′ makes it possible to promote thepenetrability of the elastomer compound through the external layer. Theuse of diameters such that D1′=D2′ makes it possible to limit the numberof different threads to be managed in the manufacture of the cord.

Advantageously, each external strand is of the type not rubberized insitu. What is meant by not rubberized in situ is that, prior to theassembly of the external layer of the cord, and prior to the assembly ofthe cord, each external strand is made up of the threads of the variouslayers and does not have any polymer compound, notably any elastomercompound.

Advantageously, the external layer is wound in a cord external-layerdirection, and each internal layer (when Q′>1) and external layer ofeach external strand is wound in the same direction of winding as thecord external-layer direction.

Three-Layer External Strands

In another particularly advantageous embodiment that improves thebreaking strength of the cord, each external strand has three layers andcomprises:

-   -   an internal layer made up of Q′≥1 internal threads,    -   an intermediate layer made up of P′>1 intermediate threads wound        around the internal layer, and    -   an external layer made up of N′>1 external threads wound around        the intermediate layer.

Each external strand has three layers, which means to say that itcomprises an assembly made up of three layers of threads, neither morenor less, which means to say that the assembly has three layers ofthreads, not two, not four, but only three. The external layer of eachstrand is wound in a helix around the intermediate layer of this strandin contact with the intermediate layer of this strand. The intermediatelayer of each strand is wound in a helix around the internal layer ofthis strand in contact with the internal layer of this strand.

In one embodiment, D1′, D2′ and D3′ each range from 0.15 mm to 0.60 mm,preferably from 0.20 mm to 0.50 mm, more preferentially from 0.23 mm to0.45 mm, and even more preferentially from 0.25 mm to 0.40 mm.

In preferred embodiments, Q′=1, 2, 3 or 4.

In one embodiment, Q′=1, P′=5 or 6 and N′=10, 11 or 12, preferably Q′=1,P′=5 or 6 and N′=10 or 11, and more preferentially Q′=1, P′=6 and N′=11.

In preferred embodiments that make it possible to increase the breakingstrength of the cord with respect to the embodiment in which Q′=1, Q′=2,3 or 4, preferably Q′=3 or 4.

In these preferred embodiments in which Q′>1, notably those in whichQ′=3 or 4, there is a risk, when the strand is insufficientlypenetrated, of seeing a significant spread of corrosive agents betweenthe Q′=3 or 4 internal threads which delimit a central capillary whichvery much encourages them to spread along each strand. This disadvantagecan be overcome by rendering the strand capable of being penetrated bythe elastomer compound which then prevents the corrosive agents fromaccessing the central capillary and, in the best of cases in which thecentral capillary is itself penetrated, prevents these corrosive agentsfrom spreading along the strand.

In preferred embodiments in which Q′>1, Q′=2, 3 or 4, P′=7, 8, 9 or 10,N′=13, 14 or 15, preferably Q′=3 or 4, P′=8, 9 or 10, N′=14 or 15, morepreferentially Q′=3, P′=8 or 9 and N′=14 or 15 and more preferentiallystill Q′=3, P′=9 and N′=15.

Advantageously, the intermediate layer of each external strand isdesaturated.

As has already been specified, by definition, a desaturated layer ofthreads is such that there is enough space between the threads to allowan elastomer compound to pass. Thus, a layer that is desaturated meansthat the threads of this layer do not touch and that there is enoughspace between two adjacent threads of the layer to allow an elastomercompound to pass through the layer. By contrast, a saturated layer ofthreads is such that there is not enough space between the threads ofthe layer to allow an elastomer compound to pass, for example becauseeach pair of two threads of the layer touch one another.

Advantageously, the inter-thread distance of the intermediate layer ofeach external strand is greater than or equal to 5 μm. For preference,the inter-thread distance of the intermediate layer of each externalstrand is greater than or equal to 15 μm, more preferentially greaterthan or equal to 35 μm, more preferentially still greater than or equalto 50 μm and highly preferentially greater than or equal to 60 μm.

The fact that the intermediate layer of each external strand isdesaturated advantageously makes it easier for the elastomer compound topass as far as the centre of each external strand, and thus render eachexternal strand less sensitive to corrosion.

In an embodiment that promotes the compromise between penetrability ofeach external strand and breaking strength, the intermediate layer ofeach external strand is incompletely unsaturated.

By definition, a layer of threads that is incompletely unsaturated issuch that there is not enough space in this layer to add in at least one(X+1)th thread having the same diameter as the X threads of the layer.In this particular instance, there is not enough space in theintermediate layer to add in at least one (P′+1)th intermediate threadhaving the same diameter as the P′ intermediate threads of theintermediate layer.

The fact that the intermediate layer of each external strand isincompletely unsaturated makes it possible to ensure an architecturalstability of the intermediate layer. Furthermore, the fact that theintermediate layer of each external strand is incompletely unsaturatedmakes it possible to ensure that each external strand comprises arelatively high number of intermediate threads and therefore exhibits arelatively high breaking strength.

Thus, advantageously, the sum SI2′ of the inter-thread distances of theintermediate layer is such that SI2′<D3′ where D3′ is the diameter ofeach external thread of each external strand, preferably SI2′≤0.8×D3′.The sum SI2′ is the sum of the inter-thread distances separating eachpair of adjacent threads of the intermediate layer. The inter-threaddistance of a layer is defined, in a section of the cord perpendicularto the main axis of the cord, as being the shortest distance which, onaverage, separates two adjacent threads of the layer. Thus, theinter-thread distance is calculated by dividing the sum SI2′ by thenumber of spaces separating the threads of the intermediate layer.Because the diameter D3′ of the external threads of the external layerof each external strand is preferentially greater than the sum SI2′, theexternal threads are prevented from penetrating the intermediate layer.This then ensures good architectural stability, thereby additionallyreducing the risk of alteration to the radial passage windows for theelastomer compound and therefore the risk of degrading the goodpenetrability of each external strand.

In another embodiment that promotes the penetrability of each externalstrand, the intermediate layer of each external strand is completelyunsaturated.

By definition, a completely unsaturated layer of threads is such thatthere is sufficient space in this layer to add in at least one (X+1)ththread having the same diameter as the X threads of the layer, it thusbeing possible for a plurality of threads to be in contact, or not incontact, with one another. In this particular instance, there is enoughspace in the intermediate layer of each external strand to add in atleast one (P′+1)th intermediate thread having the same diameter as theP′ intermediate threads of the intermediate layer.

Such an embodiment is particularly advantageous when Q′=3 and P′=8 orQ′=4 and P′=9 and when D1′=D2′. Specifically, if we had Q′=3 and P′=9 orQ′=4 and P′=10, then the intermediate layer, although desaturated,might, in certain instances, have an inter-thread distance insufficientto ensure satisfactory penetrability of the strand.

Advantageously, the external layer of each external strand isdesaturated, preferably completely unsaturated.

As has already been specified, by definition, a desaturated layer ofthreads is such that there is enough space between the threads to allowan elastomer compound to pass. Thus, a layer that is desaturated meansthat the threads of this layer do not touch and that there is enoughspace between two adjacent threads of the layer to allow an elastomercompound to pass through the layer. By contrast, a saturated layer ofthreads is such that there is not enough space between the threads ofthe layer to allow an elastomer compound to pass, for example becauseeach pair of two threads of the layer touch one another.

Advantageously, the inter-thread distance of the external layer of eachexternal strand is greater than or equal to 5 μm. For preference, theinter-thread distance of the external layer of each external strand isgreater than or equal to 15 μm, more preferentially greater than orequal to 35 μm, more preferentially still greater than or equal to 50 μmand highly preferentially greater than or equal to 60 μm.

The fact that the external layer of each external strand is desaturatedadvantageously makes it easier for the elastomer compound to pass as faras the centre of each external strand, and thus render each externalstrand less sensitive to corrosion.

By definition, a completely unsaturated layer of threads is such thatthere is sufficient space in this layer to add in at least one (X′+1)ththread having the same diameter as the X′ threads of the layer, it thusbeing possible for a plurality of threads to be in contact, or not incontact, with one another. In this particular instance, there is enoughspace in the external layer of each external strand to add in at leastone (N′+1)th external thread having the same diameter as the N′ externalthreads of the external layer.

The fact that the external layer of each external strand is completelyunsaturated makes it possible to maximize the penetration of theelastomer compound into each external strand, and thus render eachexternal strand even less sensitive to corrosion.

Thus, advantageously, the sum SI3′ of the inter-thread distances of theexternal layer of each external strand is such that SI3′≥D3′. The sumSI3′ is the sum of the inter-thread distances separating each pair ofadjacent threads of the external layer. The inter-thread distance of alayer is defined, in a section of the cord perpendicular to the mainaxis of the cord, as being the shortest distance which, on average,separates two adjacent threads of the layer. Thus, the inter-threaddistance is calculated by dividing the sum SI3′ by the number of spacesseparating the threads of the external layer.

In preferred embodiments, each internal thread of each external strandhas a diameter D1′ greater than or equal to the diameter D2′ of eachintermediate thread of each external strand. The use of diameters suchthat D1′>D2′ makes it possible to promote the penetrability of theelastomer compound through the intermediate layer. The use of diameterssuch that D1′=D2′ makes it possible to limit the number of differentthreads to be managed in the manufacture of the cord.

In preferred embodiments, each internal thread of each external strandhas a diameter D1′ greater than or equal to the diameter D3′ of eachexternal thread of each external strand. The use of diameters such thatD1>D3′ makes it possible to promote the penetrability of the elastomercompound through the external layer. The use of diameters such thatD1′=D3′ makes it possible to limit the number of different threads to bemanaged in the manufacture of the cord.

In preferred embodiments, each intermediate thread of each externalstrand has a diameter D2′ equal to the diameter D3′ of each externalthread of each external strand. The use of diameters such that D2′=D3′makes it possible to limit the number of different threads to be managedin the manufacture of the cord.

Advantageously, each external strand is of the type not rubberized insitu. What is meant by not rubberized in situ is that, prior to theassembly of the external layer of the cord, and prior to the assembly ofthe cord, each external strand is made up of the threads of the variouslayers and does not have any polymer compound, notably any elastomercompound.

Advantageously, the external layer of the cord is wound in a cordexternal-layer direction, and each internal layer (when Q′>1),intermediate layer and external layer of each external strand is woundin the same direction of winding as the cord external-layer direction.

In one embodiment, the cord internal-layer direction and the cordexternal-layer direction are opposite directions. In this embodiment,the risk of potential undesired slippage of the external strands in thegrooves formed between the internal strands as a result of a crossingbetween the internal and external strands is reduced.

In another embodiment, the cord internal-layer direction and the cordexternal-layer direction are the same. In this embodiment, manufactureis relatively easy because, unlike in the previous embodiment, there isno need to differentiate between the directions of winding of theinternal and external layers of the cord. Nevertheless, areas of contactbetween the external threads of the external layers of the internal andexternal strands are relatively long and this may, with certaincombinations of pitch, diameter and architecture of the cords, give riseto assembly defects caused, for example, by undesired slippage of theexternal strands in the grooves formed between the internal strands.

Tyre According to the Invention

Another subject of the invention is a tyre comprising a cord as definedabove.

The cord is most particularly intended for industrial vehicles selectedfrom heavy vehicles such as “heavy-duty vehicles”—i.e. undergroundtrains, buses, road haulage vehicles (lorries, tractors, trailers),off-road vehicles —, agricultural vehicles or construction plantvehicles, or other transport or handling vehicles.

As a preference, the tyre is for a vehicle of the construction planttype. The tyre has a size of the W R U type in which, as is known tothose skilled in the art, W denotes:

-   -   the nominal aspect ratio H/B as defined by the ETRTO, when it is        in the form H/B, H being the cross-sectional height of the tyre        and B being the cross-sectional width of the tyre,    -   H.00 or B.00, when it is in the form H.00 or B.00, in which H=B,        H and B being as defined above,        U represents the diameter, in inches, of the rim seat on which        the tyre is intended to be mounted, and R denotes the type of        carcass reinforcement of the tyre, in this case radial. Examples        of such dimensions are, for example, 40.00 R 57 or else 59/80 R        63.

Preferably, U≥35, more preferentially U≥49 and even more preferentiallyU≥57.

Advantageously, the tyre comprises a carcass reinforcement anchored intwo beads and surmounted radially by a crown reinforcement which isitself surmounted by a tread, the crown reinforcement being joined tothe said beads by two sidewalls and comprising at least one cord asdefined above.

Advantageously, the carcass reinforcement comprises at least one carcassply comprising filamentary metal carcass reinforcing elements arrangedsubstantially parallel to one another in the carcass ply, eachfilamentary metal carcass reinforcing element making an angle of between80° and 90° with the circumferential direction of the tyre.

Advantageously, the crown reinforcement comprises a workingreinforcement comprising at least one cord as defined above.

Advantageously, the working reinforcement comprises at least one workingply comprising filamentary metal working reinforcing elements arrangedsubstantially parallel to one another, each filamentary metal workingreinforcing element making an angle at most equal to 60°, preferablyranging from 15° to 40° with the circumferential direction of the tyreand being formed by a cord as defined above.

In one advantageous embodiment, the working reinforcement comprises atleast first and second working plies, each first and second working plyrespectively comprising first and second filamentary metal workingreinforcing elements arranged substantially parallel to one another ineach first and second working ply, each first and second filamentarymetal working reinforcing element making an angle at most equal to 60°,preferably ranging from 15° to 40° with the circumferential direction ofthe tyre and being formed by a cord as defined above.

Advantageously, the crown reinforcement comprises a protectivereinforcement comprising at least one protective ply comprisingfilamentary metal protective reinforcing elements arranged substantiallyparallel to one another, each filamentary metal protective reinforcingelement making an angle at least equal to 10° preferably ranging from10° to 35° and preferentially from 15° to 30° with the circumferentialdirection of the tyre.

In one advantageous embodiment, the protective reinforcement comprisesfirst and second protective plies, each first and second protective plyrespectively comprising first and second filamentary metal protectivereinforcing elements arranged substantially parallel to one another ineach first and second protective ply, each first and second filamentarymetal protective reinforcing element making an angle at least equal to10°, preferably ranging from 10° to 35° and preferentially from 15° to30° with the circumferential direction of the tyre.

In a preferred embodiment, the protective reinforcement is interposedradially between the tread and the working reinforcement.

Advantageously, the crown reinforcement comprises an additionalreinforcement comprising at least one additional ply comprisingadditional filamentary metal reinforcing elements arranged substantiallyparallel to one another in the additional ply, each additionalfilamentary metal reinforcing element making an angle at most equal to10°, preferably ranging from 5° to 10° with the circumferentialdirection of the tyre.

In one advantageous embodiment, the additional reinforcement comprisesfirst and second additional plies, each first and second additional plyrespectively comprising first and second additional filamentary metalreinforcing elements arranged substantially parallel to one another ineach first and second additional ply, each first and second additionalfilamentary metal reinforcing element making an angle at most equal to10°, preferably ranging from 5° to 10° with the circumferentialdirection of the tyre.

The invention will be better understood on reading the followingdescription, given solely by way of non-limiting example and withreference to the drawings.

EXAMPLE OF A TYRE ACCORDING TO THE INVENTION

A frame of reference X, Y, Z corresponding to the usual respectivelyaxial (X), radial (Y) and circumferential (Z) orientations of a tyre hasbeen depicted in the figures.

The “median circumferential plane” M of the tyre is the plane which isnormal to the axis of rotation of the tyre and which is situatedequidistant from the annular reinforcing structures of each bead, andpasses through the middle of the crown reinforcement.

FIGS. 1 and 2 depict a tyre according to the invention and denoted bythe general reference 10.

The tyre 10 is for a heavy vehicle of construction plant type, forexample of “dumper” type. Thus, the tyre 10 has a dimension of the type53/80R63.

The tyre 10 has a crown 12 reinforced by a crown reinforcement 14, twosidewalls 16 and two beads 18, each of these beads 18 being reinforcedwith an annular structure, in this instance a bead wire 20. The crownreinforcement 14 is surmounted radially by a tread 22 and connected tothe beads 18 by the sidewalls 16. A carcass reinforcement 24 is anchoredin the two beads 18 and is in this instance wound around the two beadwires 20 and comprises a turnup 26 positioned towards the outside of thetyre 10, which is shown here fitted onto a wheel rim 28. The carcassreinforcement 24 is surmounted radially by the crown reinforcement 14.

The carcass reinforcement 24 comprises at least one carcass ply 30comprising filamentary metal carcass reinforcing elements 31 arrangedsubstantially parallel to one another in the carcass ply 30 andextending from one bead 18 to the other so as to form an angle ofbetween 800 and 90 with the circumferential direction Z of the tyre 10.

The tyre 10 also comprises a sealing ply 32 made up of an elastomer(commonly known as “inner liner”) which defines the radially internalface 34 of the tyre 10 and which is intended to protect the carcass ply30 from the diffusion of air coming from the space inside the tyre 10.

The crown reinforcement 14 comprises, radially from the outside towardsthe inside of the tyre 10, a protective reinforcement 36 arrangedradially on the inside of the tread 22, a working reinforcement 38arranged radially on the inside of the protective reinforcement 36 andan additional reinforcement 50 arranged radially on the inside of theworking reinforcement 38. The protective reinforcement 36 is thusinterposed radially between the tread 22 and the working reinforcement38. The working reinforcement 38 is interposed radially between theprotective reinforcement 36 and the additional reinforcement 50.

The protective reinforcement 36 comprises first and second protectiveplies 42, 44, the first ply 42 being arranged radially on the inside ofthe second ply 44. Each first and second protective ply 42, 44respectively comprises first and second filamentary metal protectivereinforcing elements 43, 45 arranged substantially parallel to oneanother in each first and second protective ply 42, 44. Each first andsecond filamentary metal protective reinforcing element 43, 45 makes anangle at least equal to 10°, preferably ranging from 10° to 35° andpreferentially from 15° to 30°, with the circumferential direction Z ofthe tyre.

The working reinforcement 38 comprises first and second working plies46, 48, the first ply 46 being arranged radially on the inside of thesecond ply 48. Each ply 46, 48 comprises at least one cord 60. Eachfirst and second working ply 46, 48 respectively comprises first andsecond filamentary metal working reinforcing elements 47, 49 arrangedsubstantially parallel to one another in each first and second workingply 46, 48. Each first and second filamentary metal working reinforcingelement 47, 49 is formed here by a cord 60 described hereinafter.

Each first and second filamentary metal working reinforcing element 47,49 makes an angle at most equal to 60°, preferably ranging from 15° to40°, with the circumferential direction Z of the tyre 10. Optionally,the first and second filamentary metal working reinforcing elements 47,49 are crossed from one working ply to the other.

The additional reinforcement 50, also referred to as the limiting block,the function of which is to partially react the mechanical stresses ofinflation, comprises first and second additional plies 52, 54, eachfirst and second additional ply 52, 54 respectively comprising first andsecond additional filamentary metal reinforcing elements 53, 55 arrangedsubstantially parallel to one another in each first and secondadditional ply 52, 54. Each first and second additional filamentarymetal reinforcing element 53, 55 makes an angle at most equal to 10°,preferably ranging from 5° to 10°, with the circumferential direction Zof the tyre 10. The additional filamentary metal reinforcing elementsare, for example, as described in FR 2 419 181 or FR2419182.

Cord According to a First Embodiment of the Invention

FIG. 3 depicts the cord 60 according to a first embodiment of theinvention.

The cord 60 is metal and of the multi-strand type with two cylindricallayers. Thus, it will be understood that there are two layers, not more,not less, of strands of which the cord 60 is made. The layers of strandsare adjacent and concentric. The cord 60 is devoid of polymer compoundand of elastomer compound when it is not integrated into the tyre.

The cord 60 comprises an internal layer CI of the cord 60, and anexternal layer CE of the cord 60. The internal layer CI is made up ofJ>1 internal strands TI, namely of several internal strands TI, wound ina helix. The external layer CE is made up of L>1 external strands,namely of several external strands TE wound in a helix around theinternal layer CI. In this instance, J=2, 3 or 4, preferably J=3 or 4.In addition, L=7, 8, 9 or 10, preferably L=8, 9 or 10. With J=3, L=7, 8or 9 and in this instance and here J=3, L=8.

The cord 60 also comprises a wrapper F made up of a single wrappingwire.

The internal layer CI is wound in a helix in a direction of winding ofthe internal layer of the cord, here the direction S. The internalstrands TI are wound in a helix with a pitch PI such that 10 mm≤PI≤65 mmand preferably 10 mm≤PI≤45 mm. Here, PI=15 mm. The helix angle α of eachinternal strand TI in the internal layer CI of the cord 60 with a verylow modulus ranges from 3° to 42° and in this instance α=19.8°.

The external layer CE is wound in a helix around the internal layer CIin a direction of winding of the external layer of the cord that is theopposite of the direction of winding of the internal layer of the cord,here the direction Z. The external strands TE are wound in a helixaround the internal strand TI with a pitch PE such that 30 mm≤PE≤65 mmand preferably 30 mm≤PE≤60 mm. Here, PE=40 mm. The helix angle α′ ofeach external strand TE in the external layer CE of the cord 60 rangesfrom 7° to 38° and, in the case of the cord 60 with a very low modulus,ranges from 13° to 38° and in this instance α′=20.0°.

The wrapper F is wound around the external layer CE in a direction ofwinding of the wrapper, here the opposite to the direction of winding ofthe external layer CE, in this instance in the S-direction. The wrappingwire is wound in a helix around the external strands TE with a pitch PFsuch that 2 mm≤PF≤10 mm and preferably, 3 mm≤PF≤8 mm. Here, PF=5.1 mm.

The assembly made up of the internal CI and external CE layers, whichmeans to say the cord 60 without the wrapper F, has a diameter D greaterthan or equal to 4 mm, preferably greater than or equal to 4.5 mm, andless than or equal to 7 mm, preferably less than or equal to 6.5 mm.Here, D=6.1 mm.

The internal layer CI of internal strands TI has a diameter DI. Eachexternal strand TE has a diameter DE. In this instance, DI=3.18 mm,DE=1.46 mm.

The external layer CE of the cord 60 is desaturated and completelyunsaturated. The mean inter-strand distance E separating two adjacentexternal strands TE is therefore greater than or equal to 30 μm. As apreference, the mean inter-strand distance E separating two adjacentexternal strands TE is greater than or equal to 70 μm, morepreferentially than/to 100 μm, more preferentially still than/to 150 μmand highly preferentially than/to 200 μm. Here, E=241 μm. The sum SIE ofthe inter-thread distances E of the external layer CE is greater thanthe diameter DE of the external strands of the external layer CE. Here,the sum SIE=8×0.241=1.93 mm, which is a value strictly greater thanDE=1.46 mm.

Internal Strands TI of the Cord 60

Each internal strand TI has two layers. Each internal strand TIcomprises, here is made up of, two layers, not more, not less.

Each internal strand TI comprises an internal layer C1 made up of Q>1internal threads F1 and an external layer C2 made up of N>1 externalthreads F2 wound in a helix around and in contact with the internallayer C1.

Q=2, 3 or 4, preferably Q=3 or 4. N=7, 8, 9 or 10, preferably N=8, 9 or10. With Q=3, N=7, 8 or 9, and in this instance Q=3, N=8.

The internal layer C1 of each internal strand TI is wound in a helix ina direction of winding of the internal layer C1 of the internal strandTI that is identical to the direction of winding of the internal layerC1 of the cord, here in the S-direction. The Q internal threads F1 areassembled within each internal strand TI at a pitch p1 such that 2mm≤p1≤20 mm. Here, p1=3 mm. The helix angle β of each internal thread F1in the internal layer C1 within each internal strand TI ranges from 4°to 25°, here β=23.4°.

The external layer C2 of each internal strand TI is wound around and incontact with the internal layer C1 in a direction of winding of theexternal layer C2 of the internal strand TI that is identical to thedirection of winding of the internal layer C1 of the cord, here in theS-direction. The N external threads F2 are wound in a helix around the Qinternal threads F1 and are assembled within each internal strand TI ata pitch p2 such that 4 mm≤p2≤40 mm. Here, p2=6 mm. The helix angle γ ofeach external thread F2 in the external layer C2 within each internalstrand TI ranges from 6° to 31°, here γ=30.2°.

11°≤2α+β+γ≤110° and because Q>1, 16°≤2α+β+γ≤110°. In the embodiment ofthe cord 60 with a very low modulus with Q>1, 23°≤2α+β+γ≤110°. In thisparticular instance, 2α+β+γ=93.2°.

Each internal F1 and external F2 thread of each internal strand TIrespectively has a diameter D1, D2. Each diameter of the internalthreads D1 and external threads D2 of each internal strand TI rangesfrom 0.15 mm to 0.60 mm, preferably from 0.20 mm to 0.50 mm, morepreferentially from 0.23 mm to 0.45 mm and more preferentially stillfrom 0.25 mm to 0.40 mm. Each internal thread F1 of each internal strandTI has a diameter D1 greater than or equal to, here equal to, thediameter D2 of each external thread F2 of each internal strand TI.

In this instance, D1=D2=0.35 mm.

Because of the relatively short pitch p2, the external layer C2 of eachinternal strand TI is desaturated and incompletely unsaturated. Theinter-thread distance I2 of the external layer C2 which on averageseparates the N external threads is greater than or equal to 5 μm. Theinter-thread distance I2 is preferably greater than or equal to 15 μmand is here equal to 29 μm. The sum SI2 of the inter-thread distances I2of the external layer C2 is greater than the diameter d2 of the externalthreads F2 of the external layer C2. Here, the sum SI2=8×0.029=0.23 mm,which is a value strictly less than D2=0.35 mm.

Also, 25 GPa≤EI≤180 GPa, preferably 36 GPa≤EI≤180 GPa and in theembodiment of the cord 60 with a very low modulus, 25 GPa≤EI≤180 GPa,preferably 36 GPa≤EI≤175 GPa. Here, the internal layer has a relativelylow modulus and 25 GPa≤EI≤94 GPa, preferably 36 GPa≤EI≤94 GPa. In thisinstance, EI=53 GPa.

External Strands TE of the Cord 60

Each external strand TE has two layers. Thus, each external strand TEcomprises, here is made up of, two layers, not more, not less.

Each external strand TE comprises an internal layer C1′ made up of Q′≥1internal threads F1′ and an external layer C2′ made up of N′>1 externalthreads F2′ wound in a helix around and in contact with the internallayer C1′.

Q′=2, 3 or 4, preferably Q′=3 or 4. N′=7, 8, 9 or 10, preferably N′=8, 9or 10. With Q′=3, N′=7, 8 or 9, and in this instance Q′=3, N′=8.

The internal layer C1′ of each external strand TE is wound in a helix ina direction of winding of the internal layer C1′ of the external strandTE that is identical to the direction of winding of the external layerCE of the cord, here in the Z-direction. The Q′ internal threads F1′ areassembled within each external strand TE at a pitch p1′ such that 2mm≤p1′≤20 mm, preferably 5 mm≤p1′≤20 mm. Here, p1′=10 mm. The helixangle β of each internal thread F1′ in the internal layer C1′ withineach external strand TE ranges from 4° to 25°, preferably from 4° to17°, here β′=7.3°.

The external layer C2′ of each external strand TE is wound around and incontact with the internal layer C1′ in a direction of winding of theexternal layer C2′ of the external strand TE that is identical to thedirection of winding of the external layer CE of the cord, here in theZ-direction. The N′ external threads F2′ are wound in a helix around theQ′ internal threads F1′ and are assembled within each external strand TEat a pitch p2′ such that 4 mm≤p2′≤40 mm. Here, p2′=20 mm. The helixangle γ′ of each external thread F2′ in the external layer C2′ withineach external strand TE ranges from 5° to 31°, here γ′=9.8°.

23°≤2α′+β′+γ′≤97° and because Q′>1, 28°≤2α′+β′+γ′≤97° and, in theembodiment of the cord 60 with a very low modulus, 43°≤2α′+β′+γ′≤97°. Inthis particular instance, 2α′+β′+γ′=57.1°.

Each internal F1′ and external F2′ thread of each external strand TErespectively has a diameter D1′, D2′. Each diameter of the internalthreads D1′ and external threads D2′ of each external strand TE rangesfrom 0.15 mm to 0.60 mm, preferably from 0.20 mm to 0.50 mm, morepreferentially from 0.23 mm to 0.45 mm and more preferentially stillfrom 0.25 mm to 0.40 mm. Each Q′ internal thread F1′ of each externalstrand TI′ has a diameter D1′ greater than or equal to, here equal to,the diameter D2′ of each external thread F2′ of each external strand TE.In this instance, D1′=D2′=0.35 mm.

The external layer C2′ of each external strand TE is desaturated andcompletely unsaturated. The inter-thread distance I2′ of the externallayer C2′ which on average separates the N′ external threads is greaterthan or equal to 5 μm. The inter-thread distance I2′ is preferablygreater than or equal to 15 μm, more preferentially greater than orequal to 35 μm, more preferentially still greater than or equal to 50 μmand highly preferentially greater than or equal to 60 μm and is hereequal to 69 μm. The sum SI2′ of the inter-thread distances I2′ of theexternal layer C2′ is greater than the diameter D2 of the externalthreads F2′ of the external layer C2′. Here, the sum SI2′=8×0.069=0.55mm, which is a value strictly greater than D2′=0.35 mm.

Each thread F1, F2, F1′, F2′ has a breaking strength, denoted Rm, suchthat 2500 S Rm S 3100 MPa. The steel for these threads is said to be ofSHT (“Super High Tensile”) grade. Other threads may be used, for examplethreads of an inferior grade, for example of NT (“Normal Tensile”) or HT(“High Tensile”) grade, just as may threads of a superior grade, forexample of UT (“Ultra Tensile”) or MT (“Mega Tensile”) grade.

51°≤2α+β+γ+2α′+β′+γ′≤184° and because Q>1 et Q′>1,68°≤2α+β+γ+2α′+β′+γ′≤184°. In the embodiment of the cord 60 with a verylow modulus, 85°≤2α+β+γ+2α′+β′+γ′≤184° and because Q>1 and Q′>1,110°≤2α+β+γ+2α′+β′+γ′≤184°. In this particular instance,2α+β+γ+2α′+β′+γ′=150.3°.

1.21≤EC/EI, preferably 1.21≤EC/EI≤3.00 and here EC/EI=1.62.

Also, 50 GPa≤EC≤160 GPa and in the embodiment of the cord 60 with a verylow modulus, 50 GPa≤EC≤89 GPa. Here, EC=86 GPa.

Method for Manufacturing the Cord According to the Invention

The cord according to the invention is manufactured using a methodcomprising steps well known to those skilled in the art.

In a step for manufacturing the internal strands using the followingsteps, preferably carried out in line and continuously:

-   -   first of all, a first step of assembling, by twisting, the Q        internal threads F1 of the internal layer C1 at the pitch p1 and        in the S-direction to form the internal layer C1 at a first        assembling point;    -   followed by a second step of assembling, by twisting, the N        external threads F2 around the N internal threads F1 of the        internal layer C1 at the pitch p2 and in the S-direction to form        the external layer C2 and each internal strand TI at a second        assembling point;    -   preferably a final twist-balancing step.

In a step for manufacturing the external strands using the followingsteps, preferably carried out in line and continuously:

-   -   first of all, a first step of assembling, by twisting, the Q′        internal threads F1′ of the internal layer C1′ at the pitch p1′        and in the Z-direction to form the internal layer C1′ at a first        assembling point;    -   followed by a second step of assembling, by twisting, the N′        external threads F2′ around the N′ internal threads F1′ of the        internal layer C1′ at the pitch p2′ and in the Z-direction to        form the external layer C2′ and each external strand TE at a        second assembling point;    -   preferably a final twist-balancing step.

What is meant here by “twist balancing” is, as is well known to thoseskilled in the art, the cancellation of the residual twist torques (orthe elastic return of the twist) applied to each thread of the strand,in the intermediate layer as in the external layer.

After this final twist-balancing step, the manufacture of each strand iscomplete. Each strand is wound onto one or more receiving reels, forstorage, prior to the later operation of assembling the elementarystrands in order to obtain the multi-strand cord.

In order to manufacture the multi-strand cord of the invention, themethod, as is well known to those skilled in the art, is to cabletogether the strands previously obtained, using cabling machines ratedfor assembling strands.

In a step of manufacturing the internal layer C1, the Q internal strandsTI are assembled by cabling at the pitch PI and in the S-direction toform the internal layer C1 at a first assembling point. In theembodiments in which the pitch PI is relatively short and therefore inwhich α is relatively high, the Q internal strands TI are assembled bytwisting in order to limit the risk of instability of the internal layerC1 of the strands TI.

Then, in a later manufacturing step, the L external strands TE areassembled by cabling around the internal layer C1 at the pitch PE and inthe Z-direction to form the assembly of the layers C1 and CE. In theembodiments in which the pitch PE is relatively short and therefore inwhich α′ is relatively high, the L external stands TE are assembled bytwisting in order to limit the risk of instability of the external layerCE of the strands TE.

In a second manufacturing step, the wrapper F is wound, at the pitch PFand in the S-direction, around the assembly previously obtained.

The cord is then incorporated by skimming into composite fabrics formedfrom a known composition based on natural rubber and carbon black asreinforcing filler, conventionally used for manufacturing crownreinforcements of radial tyres. This compound essentially contains, inaddition to the elastomer and the reinforcing filler (carbon black), anantioxidant, stearic acid, an extender oil, cobalt naphthenate asadhesion promoter, and finally a vulcanization system (sulfur,accelerator and ZnO).

The composite fabrics reinforced by these cords have an elastomercompound matrix formed from two thin layers of elastomer compound whichare superposed on either side of the cords and which have a thickness ofbetween 1 and 4 mm inclusive, respectively. The skim-coating pitch (thepitch at which the cords are laid in the elastomer compound fabric)ranges from 4 mm to 8 mm.

These composite fabrics are then used as working ply in the crownreinforcement during the method of manufacturing the tyre, the steps ofwhich are otherwise known to a person skilled in the art.

Cord According to a 2^(nd) Embodiment of the Invention

A low-modulus cord 61 according to a second embodiment of the inventionwill be described. Elements similar to those of the first embodiment aredenoted by identical references.

Amongst the differences between the cords 60 and 61, it will be notedthat the low-modulus cord 61 is such that the helix angle α ranges from3° to 36° and in this instance α=10°, and that the helix angle α′ rangesfrom 9° to 27° and in this instance α′=16.1°.

It will also be noted that, in the case of the cord 61 with a lowmodulus, 13°≤2α+β+γ≤110° and because Q>1, 16°≤2α+β+γ≤110°. In thisparticular instance, 2α+β+γ=46.2°.

It will also be noted that, in the embodiment of the cord 61 with a lowmodulus, 25 GPa≤EI≤180 GPa, preferably 64 GPa≤EI≤180 GPa. Because theinternal layer has a relatively high modulus, 95 GPa≤EI≤180 GPa. In thisinstance, EI=148 GPa.

It will also be noted that, in the case of the cord 61 with a lowmodulus, 31°≤2α′+β′+γ′≤71° and because Q′>1, 39°≤2α′+β′+γ′≤71°. In thisparticular instance, 2α′+β′+γ′=54.3°.

It will also be noted that, in the case of the cord 61 with a lowmodulus, 65°≤2α+β+γ+2α′+β′+γ′≤153° and because Q>1 and Q′>1,79°≤2α+β+γ+2α′+β′+γ′≤153°. In this particular instance,2α+β+γ+2α′+β′+γ′=100.5°.

It will be noted that 0.60≤EC/EI≤1.20 and here EC/EI=0.86.

It will be noted that, in the embodiment of the cord 61 with a lowmodulus, 90 GPa≤EC≤130 GPa. Here, EC=127 GPa.

Cord According to a 3^(rd) Embodiment of the Invention

FIG. 6 depicts a medium-modulus cord 62 according to a third embodimentof the invention. Elements similar to those of the cords alreadydescribed are denoted by identical references.

Amongst the differences between the cords 60 and 62, it will be notedthat the helix angle α of each internal strand TI in the internal layerC1 of the cord 62 with a medium modulus ranges from 3° to 24° and inthis instance α=9.1°. It will also be noted that the helix angle α′ ofeach external strand TE in the external layer CE of the cord 62 with amedium modulus ranges from 7° to 22° and in this instance α′=16.2°.

It will also be noted that, in the case of the cord 62 with a mediummodulus, 11°≤2α+β+γ≤64° and because Q>1, 16°≤2α+β+γ≤63° and in thisinstance 2α+β+γ=29.6°.

It will also be noted that, in the embodiment of the cord 62 with amedium modulus, 78 GPa≤EI≤180 GPa, preferably 100 GPa≤EI≤180 GPa. Here,the internal layer has a relatively high modulus, 95 GPa≤EI≤180 GPa andin this instance EI=173 GPa.

It will also be noted that, in the embodiment of the cord 62 with amedium modulus, 23°≤2α′+β′+γ′≤58° and because Q′>1, 27°≤2α′+β′+γ′≤58°.In this particular instance, 2α′+β′+γ′=49.5°.

It will also be noted that, in the embodiment of the cord 62 with amedium modulus, 45°≤2α+β+γ+2α′+β′+γ′≤108° and because Q>1 and Q′>1,60°≤2α+β+γ+2α′+β′+γ′≤108°. In this particular instance,2α+β+γ+2α′+β′+γ′=79.1°.

It will also be noted that 0.60≤EC/EI≤1.20, preferably 0.80≤EC/EI≤1.15and here, EC/EI=0.86.

It will be noted, in the embodiment of the cord 62 with a mediummodulus, that 131 GPa≤EC≤160 GPa. Here, EC=149 GPa.

Cord According to a 4^(th) Embodiment of the Invention

A very low-modulus cord 63 according to a fourth embodiment of theinvention will now be described. Elements similar to those of the cordsalready described are denoted by identical references.

Amongst the differences between the cords 60 and 63, it will be notedthat, because the internal layer has a relatively high modulus, 95GPa≤EI≤180 GPa, preferably 95 GPa≤EI≤175 GPa. In this instance, EI=158GPa.

It will also be noted that EC/EI≤0.59, preferably 0.40≤EC/EI≤0.59 andhere EC/EI=0.50.

Cord According to a 5^(th) Embodiment of the Invention

A very low-modulus cord 64 according to a fifth embodiment of theinvention will now be described. Elements similar to those of the cordsalready described are denoted by identical references.

Amongst the differences between the cords 62 and 64, it will be notedthat the cord 64 is such that J=4 and L=9 and that each thread F1, F1′,F2, F2′ is such that D1=D1′=D2=D2′=0.40 mm.

Cord According to a 6^(th) Embodiment of the Invention

A low-modulus cord 65 according to a sixth embodiment of the inventionwill now be described. Elements similar to those of the cords alreadydescribed are denoted by identical references.

Amongst the differences between the cords 61 and 65, it will be notedthat, because the internal layer has a relatively low modulus, 25GPa≤EI≤94 GPa and in this instance, EI=59 GPa.

It will also be noted that, in the embodiment of the cord 65,1.21≤EC/EI, preferably 1.21≤EC/EI≤3.00 and here EC/EI=1.63.

Cord According to a 7^(th) Embodiment of the Invention

A medium-modulus cord 66 according to a seventh embodiment of theinvention will now be described. Elements similar to those of the cordsalready described are denoted by identical references.

Amongst the differences between the cords 62 and 66, it will be notedthat the cord 66 is such that J=4 and L=10 and that each thread F1, F1′,F2, F2′ is such that its diameter D1, D1′, D2, D2′ ranges from 0.25 mmto 0.40 mm and here D1=D1′=D2=D2′=0.35 mm.

Cord According to a 8^(th) Embodiment of the Invention

FIG. 8 depicts the cord 160 according to an eighth embodiment of theinvention.

The cord 160 is metal and of the multi-strand type with two cylindricallayers. Thus, it will be understood that there are two layers, not more,not less, of strands of which the cord 160 is made. The layers ofstrands are adjacent and concentric. The cord 160 is devoid of polymercompound and of elastomer compound when it is not integrated into thetyre.

The cord 160 comprises an internal layer C1 of the cord 160, and anexternal layer CE of the cord 160. The internal layer C1 is made up ofJ>1 internal strands TI, namely of several internal strands TI, wound ina helix. The external layer CE is made up of L>1 external strands,namely of several external strands TE wound in a helix around theinternal layer C1. In this instance, J=2, 3 or 4, preferably J=3 or 4.In addition, L=7, 8, 9 or 10, preferably L=8, 9 or 10. With J=3, L=7, 8or 9 and in this instance and here J=3, L=8.

The cord 160 also comprises a wrapper F made up of a single wrappingwire.

The internal layer CI is wound in a helix in a direction of winding ofthe internal layer of the cord, here the direction S. The internalstrands TI are wound in a helix with a pitch PI such that 10 mm≤PI≤65 mmand preferably 10 mm≤PI≤45 mm. Here, PI=20 mm. The helix angle α of eachinternal strand TI in the internal layer CI of the cord 160 ranges from4° to 41° and, in the embodiment of the cord 160 with a low modulus,from 4° to 31°, in this instance α=13.4°.

The external layer CE is wound in a helix around the internal layer CIin a direction of winding of the external layer of the cord that is theopposite of the direction of winding of the internal layer of the cord,here the direction Z. The external strands TE are wound in a helixaround the internal strand TI with a pitch PE such that 30 mm≤PE≤65 mmand preferably 30 mm≤PE≤60 mm. Here, PE=40 mm. The helix angle α′ ofeach external strand TE in the external layer CE of the cord 160 rangesfrom 130 to 360 and, in the embodiment of the cord 160 with a lowmodulus, from 13° to 32°, in this instance α′=19.1°.

The wrapper F is wound around the external layer CE in a direction ofwinding of the wrapper, here the opposite to the direction of winding ofthe external layer CE, in this instance in the S-direction. The wrappingwire is wound in a helix around the external strands TE with a pitch PFsuch that 2 mm≤PF≤10 mm and preferably 3 mm≤PF≤8 mm. Here, PF=5.1 mm.

The assembly made up of the internal CI and external CE layers, whichmeans to say the cord 160 without the wrapper F, has a diameter Dgreater than or equal to 4 mm, preferably greater than or equal to 4.5mm, and less than or equal to 7 mm, preferably less than or equal to 6.5mm. Here, D=6 mm.

The internal layer C1 of internal strands TI has a diameter DI. Eachexternal strand TE has a diameter DE. In this case, DI=2.83 mm, DE=1.58mm.

The external layer CE of the cord 160 is desaturated and incompletelyunsaturated.

Here, the mean inter-strand distance E separating two adjacent externalstrands TE is such that E=29 μm. The sum SIE of the inter-threaddistances E of the external layer CE is less than the diameter DE of theexternal strands of the external layer CE. Here, the sumSIE=8×0.029=0.23 mm, which is a value strictly less than DE=1.58 mm.

Internal Strands TI of the Cord 160

Each internal strand TI has three layers. Each internal strand TIcomprises, here is made up of, three layers, not more, not less.

Each internal strand TI comprises an internal layer C1 made up of Q>1internal threads F1, an intermediate layer C2 made up of P>1intermediate threads F2 wound in a helix around and in contact with theinternal layer C1, and an external layer C3 made up of N>1 externalthreads F3 wound in a helix around and in contact with the intermediatelayer C2.

Q=1, P=5 or 6 and N=10, 11 or 12, preferably Q=1, P=5 or 6, N=10 or 11and more preferentially here Q=1, P=6 and N=11.

In the instance in which Q>1, the internal layer C1 of each internalstrand TI is wound in a helix in a direction of winding of the internallayer C1 of the internal strand TI that is identical to the direction ofwinding of the internal layer C1 of the cord, here in the S-direction.Here, the Q=1 internal thread F1 is assembled within each internalstrand TI at an infinite pitch such that β=0.

The intermediate layer C2 of each internal strand TI is wound around andin contact with the internal layer C1 in a direction of winding of theintermediate layer C2 of the internal strand TI that is identical to thedirection of winding of the internal layer CI of the cord, here in theS-direction. The P intermediate threads F2 are wound in a helix aroundthe Q=1 internal thread F1 and are assembled within each internal strandTI at a pitch p2 such that 5 mm≤p2≤20 mm. Here, p2=7.7 mm. The helixangle δ of each intermediate thread F2 in the intermediate layer C2within each internal strand TI ranges from 6° to 30°, here δ=12.2°.

The external layer C3 of each internal strand TI is wound around and incontact with the intermediate layer C2 in a direction of winding of theexternal layer C3 of the internal strand TI that is identical to thedirection of winding of the internal layer CI of the cord, here in theS-direction. The N external threads F3 are wound in a helix around the Pintermediate threads F2 and are assembled within each internal strand TIat a pitch p3 such that 10 mm≤p3≤40 mm. Here, p3=15.4 mm. The helixangle γ of each external thread F3 in the external layer C3 within eachinternal strand TI ranges from 7° to 30°, here γ=12.1°.

25°≤3α+β+γ+γ≤158° and here, because Q=1, 25°≤3α+β+δ+γ≤140°. In thisparticular instance, in this first embodiment of the cord 160 with a lowmodulus, 25°≤3α+β+δ+γ≤125° and here, because Q=1, 25°≤3α+β+δ+γ≤120°. Inthe case of the cord 160, 3α+β++γ=64.5°.

Each internal F1, intermediate F2 and external F3 thread of eachinternal strand TI respectively has a diameter D1, D2, D3. Each diameterof the internal threads D1, intermediate threads D2 and external threadsD3 of each internal strand TI ranges from 0.15 mm to 0.60 mm, preferablyfrom 0.20 mm to 0.50 mm, more preferentially from 0.23 mm to 0.45 mm andmore preferentially still from 0.25 mm to 0.40 mm. Each internal threadF1 of each internal strand TI has a diameter D1 greater than or equalto, here equal to, the diameter D2 of each intermediate thread F2 ofeach internal strand TI. Each internal thread F1 of each internal strandTI has a diameter D1 greater than or equal to, here equal to, thediameter D3 of each external thread F3 of each internal strand TI. Eachintermediate thread F2 of each internal strand TI has a diameter D2equal to the diameter D3 of each external thread F3 of each internalstrand TI. In this instance, D1=D2=D3=0.26 mm.

The intermediate layer C2 of each internal strand TI is saturated. Here,the distance I2 is approximately equal to 0.

The external layer C3 of each internal strand TI is desaturated andcompletely unsaturated. The inter-thread distance I3 of the externallayer C3 which on average separates the N external threads is greaterthan or equal to 5 μm. The inter-thread distance I3 is preferablygreater than or equal to 15 μm and is here equal to 30 μm. The sum SI3of the inter-thread distances I3 of the external layer C3 is greaterthan the diameter D3 of the external threads F3 of the external layerC3. Here, the sum SI3=11×0.030=0.33 mm, which is a value strictlygreater than D2=0.26 mm.

Also, 25 GPa≤EI≤180 GPa, preferably 36 GPa≤EI≤180 GPa and, in theembodiment of the cord 160 with a low modulus, 25 GPa≤EI≤180 GPa,preferably 64 GPa≤EI≤180 GPa. Here, the internal layer has a relativelyhigh modulus, so 95 GPa≤EI≤180 GPa. In this instance, EI=147 GPa.

External Strands TE of the Cord 160

Each external strand TE has three layers. Thus, each external strand TEcomprises, here is made up of, three layers, not more, not less.

Each external strand TE comprises an internal layer C1′ made up of Q′>1internal threads F1′, an intermediate layer C2′ made up of P′>1intermediate threads F2′ wound in a helix around and in contact with theinternal layer C1′, and an external layer C3′ made up of N′>1 externalthreads F3′ wound in a helix around and in contact with the intermediatelayer C2′.

Q′=1, P′=5 or 6 and N′=10, 11 or 12, preferably Q′=1, P′=5 or 6, N′=10or 11 and more preferentially here Q′=1, P′=6 and N′=11.

In the instance in which Q′>1, the internal layer C1′ of each externalstrand TE is wound in a helix in a direction of winding of the internallayer C1′ of the external strand TE that is identical to the directionof winding of the external layer CE of the cord, here in theZ-direction. Here, the Q′=1 internal thread F1′ is assembled within eachexternal strand TE at an infinite pitch p1′ such that β′=0.

The intermediate layer C2′ of each external strand TE is wound aroundand in contact with the internal layer C1′ in a direction of winding ofthe intermediate layer C2′ of the external strand TE that is identicalto the direction of winding of the external layer CE of the cord, herein the Z-direction. The P′ intermediate threads F2′ are wound in a helixaround the Q′=1 internal thread F1′ and are assembled within eachexternal strand TE at a pitch p2′ such that 5 mm S p2′≤20 mm. Here,p2′=7.7 mm. The helix angle δ′ of each intermediate thread F2′ in theintermediate layer C2′ within each external strand TE ranges from 6° to22°, here δ′=15.5°.

The external layer C3′ of each external strand TE is wound around and incontact with the intermediate layer C2′ in a direction of winding of theexternal layer C3′ of the external strand TE that is identical to thedirection of winding of the external layer CE of the cord, here in theZ-direction. The N′ external threads F3′ are wound in a helix around theP′ intermediate threads F2′ and are assembled within each externalstrand TE at a pitch p3′ such that 10 mm s p3′≤40 mm. Here, p3′=15.4 mm.The helix angle γ′ of each external thread F3′ in the external layer C3′within each external strand TE ranges from 7° to 22°, here γ′=14.6°.

48°≤3α′+β+δ′+γ′≤154° and here, because Q′=1, 48°≤3α′+β′+δ′+γ′≤145°.

In this particular instance, in this first embodiment of the cord 160with a low modulus, 54°≤3α′+β′+δ′+γ′≤123°, and here, because Q′=1,54°≤3α′+β′+δ′+γ′≤118°. In the case of the cord 160, 3α′+β+′+γ′=87.4°.

Each internal F1′, intermediate F2′ and external F3′ thread of eachexternal strand TE respectively has a diameter D1′, D2′, D3′. Eachdiameter of the internal threads D1′, intermediate threads D2′ andexternal threads D3′ of each external strand TE ranges from 0.15 mm to0.60 mm, preferably from 0.20 mm to 0.50 mm, more preferentially from0.23 mm to 0.45 mm and more preferentially still from 0.25 mm to 0.40mm. Each Q′ internal thread F1′ of each external strand TE has adiameter D1′ greater than or equal to the diameter D2′ of eachintermediate thread F2′ of each external strand TE. Each Q′ internalthread F1′ of each external strand TE has a diameter D1′ greater than orequal to the diameter D3′ of each external thread F3′ of each externalstrand TE. Each N′ intermediate thread F2′ of each external strand TEhas a diameter D2′ equal to the diameter D3′ of each external thread F3′of each external strand TE. In this instance, D1′=0.38 mm>D2′=D3′=0.30mm.

The intermediate layer C2′ of each external strand TE is desaturated andincompletely unsaturated. The inter-thread distance I2′ of theintermediate layer C2′ which on average separates the P′ intermediatethreads is greater than or equal to 5 μm. The inter-thread distance I2′is preferably greater than or equal to 15 μm and is here equal to 32 μm.The sum SI2′ of the inter-thread distances I2′ of the intermediate layerC2′ is greater than the diameter D2 of the intermediate threads F2′ ofthe intermediate layer C2′. Here, the sum SI2′=6×0.032=0.19 mm, which isa value strictly less than D2′=0.30 mm. In addition, the sum SI2′ of theinter-thread distances I2′ is such that SI2′<D3′ and even SI2′<0.8×D3′.

The external layer C3′ of each external strand TE is desaturated andcompletely unsaturated. The inter-thread distance I3′ of the externallayer C3′ which on average separates the N′ external threads is greaterthan or equal to 5 μm. The inter-thread distance I3′ is preferablygreater than or equal to 15 μm, more preferentially greater than orequal to 35 μm, more preferentially still greater than or equal to 50μm, and here is equal to 52 μm. The sum SI3′ of the inter-threaddistances I3′ of the external layer C3′ is greater than the diameter D3′of the external threads F3′ of the external layer C3′. Here, the sumSI3′=11×0.052=0.57 mm, which is a value strictly greater than D3′=0.30mm.

Each thread F1, F2, F3, F1′, F2′, F3′ has a breaking strength, denotedRm, such that 2500≤Rm≤3100 MPa. The steel for these threads is said tobe of SHT (“Super High Tensile”) grade. Other threads may be used, forexample threads of an inferior grade, for example of NT (“NormalTensile”) or HT (“High Tensile”) grade, just as may threads of asuperior grade, for example of UT (“Ultra Tensile”) or MT (“MegaTensile”) grade.

84°≤3α+β+γ+γ+3α′+β′+δ′+γ′≤280°. In this particular instance, because Q=1and Q′=1, 84°≤3α+β+γ+γ+3α′+β′+δ′+γ′≤246°. In the embodiment of the cord160 with a low modulus, 107°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤211° and because Q=1and Q′=1, 107°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤197° and here3α+β+δ+γ+3α′+β′+δ′+γ′=151.9°.

0.60≤EC/EI≤1.20 and here EC/EI=0.70.

Also, 50 GPa≤EC≤160 GPa and in this embodiment of the cord 160 with alow modulus, 90 GPa≤EC≤130 GPa. Here, EC=103 GPa.

Cord According to a 9^(th) Embodiment of the Invention

A low-modulus cord 161 according to a second embodiment of the inventionwill now be described. Elements similar to those of the cord 160 aredenoted by identical references.

Amongst the differences between the cords 160 and 161, it will beparticularly noted that the cord 161 is such that J=4 and L=10 and thateach thread F1, F1′, F2, F2′, F3, F3′ is such that its diameter D1, D1′,D2, D2′, D3, D3′ is such that D1=D2=D3=0.40 mm and D1′=D2′=D3′=0.30 mm.

Cord According to a 10^(th) Embodiment of the Invention

A low-modulus cord 162 according to a third embodiment of the inventionwill now be described. Elements similar to those of the cords alreadydescribed are denoted by identical references.

Amongst the differences between the cords 160 and 162, Q>1, Q=2, 3 or 4,P=7, 8, 9 or 10, N=13, 14 or 15 and here Q=3, P=8 and N=13. The Qinternal threads F1 are wound in a helix within each internal strand TIat a pitch p1 such that 5 mm≤p1≤15 mm. Here, p1=8 mm. The helix angle βof each internal thread F1 of the internal layer within each internalstrand TI ranges from 4° to 17°, here β=6.7°. The P intermediate threadsF2 are wound in a helix around the Q internal threads F1 and areassembled within each internal strand TI at a pitch p2 such that 10mm≤p2≤20 mm. Here, p2=15 mm. The helix angle δ of each intermediatethread F2 in the intermediate layer C2 within each internal strand TIranges from 8° to 22°, here δ=9.8°. The N external threads F3 are woundin a helix around the P intermediate threads F2 and are assembled withineach internal strand TI at a pitch p3 such that 10 mm≤p3≤40 mm. Here,p3=20 mm. The helix angle γ of each external thread F3 in the externallayer C3 within each internal strand TI ranges from 9° to 25°, hereγ=11.9°.

It will also be noted that, because Q>1, 36°≤3α+β+γ+γ≤158°, and in theembodiment of the cord 162 with a low modulus, 36°≤3α+β+γ+γ≤125° andhere 3α+β+δ+γ=108.5°.

It will also be noted that, because the internal layer of the cord 162has a relatively low modulus, 25 GPa≤EI≤94 GPa, preferably 64 GPa≤EI≤94GPa and here EI=82 GPa.

It will also be noted that Q′>1, Q′=2, 3 or 4, P′=7, 8, 9 or 10, N′=13,14 or 15 and here Q′=3, P′=8 and N′=13. The Q′ internal threads F1′ arewound in a helix within each external strand TE at a pitch p1′ such that5 mm≤p1′≤15 mm. Here, p1′=12 mm. The helix angle β of each internalthread F1′ of the internal layer within each external strand TE rangesfrom 4° to 20°, here β′=4.5°. The P′ intermediate threads F2′ areassembled within each external strand TE at a pitch p2′ such that 10mm≤p2′≤20 mm. Here, p2′=18 mm. The helix angle δ′ of each intermediatethread F2′ of the intermediate layer C2′ within each external strand TEranges from 8° to 22°, here δ′=8.1°. The N′ external threads F3′ areassembled within each external strand TE at a pitch p3′ such that 10mm≤p3′≤40 mm. Here, p3′=25 mm. The helix angle γ′ of each externalthread F3′ in the external layer C3′ within each external strand TEranges from 9° to 25° here γ′=9.6°.

It will also be noted that, because Q′>1, 61°≤3α′+β′+δ′+γ′≤154°, and inthe case of the cord 162 with a low modulus, 65°≤3α+β+δ+γ≤123° and here3α′+β′+δ′+γ′=71.4°.

It will also be noted that, because Q>1 and Q′>1,101°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤280°, and in the embodiment of the cord 162with a low modulus, 120°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤211° and here3α+β+δ+γ+3α′+β′+δ′+γ′=179.9°.

Also, 1.21≤EC/EI and preferably 1.21≤EC/EI≤3.00 and in the embodiment ofthe cord 162 with a low modulus, 1.21≤EC/EI≤3.00 and here EC/EI=1.29.

Cord According to a 11^(th) Embodiment of the Invention

A very low-modulus cord 163 according to a fourth embodiment of theinvention will now be described. Elements similar to those of the cordsalready described are denoted by identical references.

Amongst the differences between the cords 160 and 163, it will be notedthat the helix angle α of each internal strand TI in the internal layerCI of the cord 163 with a very low modulus ranges from 6° to 41°, inthis instance α=24.6°.

It will also be noted that the helix angle α′ of each external strand TEin the external layer CE of the cord 163 with a very low modulus from 14to 36°, in this instance α′=16.3°.

It will also be noted that Q>1, Q=2, 3 or 4, P=7, 8, 9 or 10, N=13, 14or 15 and here Q=3, P=8 and N=13. The Q internal threads F1 are wound ina helix within each internal strand TI at a pitch p1 such that 5mm≤p1≤15 mm. Here, p1=5 mm. The helix angle β of each internal thread F1of the internal layer within each internal strand TI ranges from 4° to17°, here β=12.4°. The P intermediate threads F2 are wound in a helixaround the Q internal threads F1 and are assembled within each internalstrand TI at a pitch p2 such that 10 mm≤p2≤20 mm. Here, p2=10 mm. Thehelix angle δ of each intermediate thread F2 in the intermediate layerC2 within each internal strand TI ranges from 8° to 22°, here δ=16.6°.The N external threads F3 are wound in a helix around the P intermediatethreads F2 and are assembled within each internal strand TI at a pitchp3 such that 10 mm≤p3≤40 mm. Here, p3=15 mm. The helix angle γ of eachexternal thread F3 in the external layer C3 within each internal strandTI ranges from 9° to 25°, here γ=18°.

It will also be noted that, in this embodiment of the cord 163 with avery low modulus, 29°≤3α+β+δ+γ≤158° and here because Q>1,42°≤3α+β+δ+γ≤158°. In the case of the cord 163, 3α+β+δ+γ=120.8°.

It will also be noted that, in the case of the cord 163 with a very lowmodulus having an internal layer with a relatively low modulus, 25GPa≤EI≤94 GPa, preferably 36 GPa≤EI≤94 GPa, and in this instance, EI=74GPa.

It will also be noted that, in the embodiment of the cord 163 with avery low modulus, 65°≤3α′+β′+δ′+γ′≤153° and here because Q′=1,65°≤3α′+β′+δ′+γ′≤143° and in this instance, 3α′+β′+δ′+γ′=91.8°.

It will also be noted that, because Q>1 and Q′=1,96°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤261°. In the embodiment of the cord 163 with avery low modulus, 138°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤280° and because Q>1 andQ′=1, 144°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤261° and here3α+β+δ+γ+3α′+β′+δ′+γ′=212.6°.

It will be noted that, in the embodiment of the cord 163 with a very lowmodulus, 0.60≤EC/EI≤1.20 and here EC/EI=1.08.

Also, 50 GPa≤EC≤160 GPa and in this embodiment of the cord 163 with avery low modulus, 50 GPa≤EC≤89 GPa. Here, EC=80 GPa.

Cord According to a 12^(th) Embodiment of the Invention

A very low-modulus cord 164 according to a fifth embodiment of theinvention will now be described. Elements similar to those of the cordsalready described are denoted by identical references.

Amongst the differences between the cords 163 and 164, it will be notedthat the internal layer has a relatively high modulus and is such that95 GPa≤EI≤180 GPa, preferably 95 GPa≤EI≤175 GPa. In this instance,EI=157 GPa.

It will also be noted that Q′>1, Q′=2, 3 or 4, P′=7, 8, 9 or 10, N′=13,14 or 15 and here Q′=3, P′=8 and N′=13. The Q′ internal threads F1′ arewound in a helix within each external strand TE at a pitch p1′ such that5 mm≤p1′≤15 mm. Here, p1′=8 mm. The helix angle β of each externalthread F1′ of the internal layer within each external strand TE rangesfrom 4° to 20°, here β′=7.8°. The P′ intermediate threads F2′ areassembled within each external strand TE at a pitch p2′ such that 10mm≤p2′≤20 mm. Here, p2′=15 mm. The helix angle δ′ of each intermediatethread F2′ of the intermediate layer C2′ within each external strand TEranges from 8° to 22°, here δ′=11.2°. The N′ external threads F3′ areassembled within each external strand TE at a pitch p3′ such that 10mm≤p3′≤40 mm. Here, p3′=20 mm. The helix angle γ′ of each externalthread F3′ in the external layer C3′ within each external strand TEranges from 9° to 25°, here γ′=13.7°.

It will be noted that 48°≤3α′+β′+δ′+γ′≤154° and here because Q′>1,61°≤3α′+β′+δ′+γ′≤154°. In this particular instance, in this embodimentof the cord 164 with a very low modulus, 65°≤3α′+β′+δ′+γ′≤153° and herebecause Q′>1, 78°≤3α′+β′+δ′+γ′≤153°. In the case of the cord 164,3α′+β′+δ′+γ′=130.8°.

It will be noted that 84°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤280°. In this particularinstance, because Q>1 and Q′>1, 101°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤280°. In theembodiment of the cord 164 with a very low modulus,138°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤280° and because Q>1 and Q′>1,144°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤280° and here 3α+β+δ+γ+3α′+β′+δ′+γ′=190.1°.

It will also be noted that EC/EI≤0.59, preferably 0.40≤EC/EI≤0.59 andhere EC/EI=0.49.

Cord According to a 13^(th) Embodiment of the Invention

Avery low-modulus cord 165 according to a sixth embodiment of theinvention will now be described. Elements similar to those of the cordsalready described are denoted by identical references.

Amongst the differences between the cords 163 and 165, it will be notedthat Q=1, P=5 or 6 and N=10, 11 or 12, preferably Q=1, P=5 or 6, N=10 or11 and more preferentially here Q=1, P=6 and N=11 and that the Q=1internal thread F1 is assembled within each internal strand TI at aninfinite pitch such that β=0. The P intermediate threads F2 are wound ina helix around the Q=1 internal thread F1 and are assembled within eachinternal strand TI at a pitch p2 such that 5 mm≤p2 S 20 mm. Here, p2=15mm. The helix angle δ of each intermediate thread F2 in the intermediatelayer C2 within each internal strand TI ranges from 6° to 30°, hereδ=9.6°. The N external threads F3 are wound in a helix around the Pintermediate threads F2 and are assembled within each internal strand TIat a pitch p3 such that 10 mm≤p3≤40 mm. Here, p3=25 mm. The helix angleγ of each external thread F3 in the external layer C3 within eachinternal strand TI ranges from 7° to 30°, here γ=11.4°.

It will also be noted that 25°≤3α+β+δ+γ≤158° and here because Q=1,25°≤3α+β+δ+γ≤140°. In this particular instance, in this embodiment ofthe cord 165 with a very low modulus, 29°≤3α+β+γ+γ≤158° and here becauseQ=1, 29°≤3α+β+γ+γ≤140°.

In the case of the cord 165, 3α+β+δ+γ=120.9°.

It will also be noted that Q′>1, Q′=2, 3 or 4, P′=7, 8, 9 or 10, N′=13,14 or 15 and here Q′=3, P′=8 and N′=13. The Q′ internal threads F1′ arewound in a helix within each external strand TE at a pitch p1′ such that5 mm≤p1′≤15 mm. Here, p1′=12 mm. The helix angle β of each externalthread F1′ of the internal layer within each external strand TE rangesfrom 4° to 20°, here β′=5.2°. The P′ intermediate threads F2′ areassembled within each external strand TE at a pitch p2′ such that 10mm≤p2′≤20 mm. Here, p2′=18 mm. The helix angle δ′ of each intermediatethread F2′ in the intermediate layer C2′ within each external strand TEranges from 8° to 22°, here δ′=9.4°. The N′ external threads F3′ areassembled within each external strand TE at a pitch p3′ such that 10mm≤p3′≤40 mm. Here, p3′=25 mm. The helix angle γ′ of each externalthread F3′ in the external layer C3′ within each external strand TEranges from 9° to 25°, here γ′=11°.

It will be noted that 48°≤3α′+β′+δ′+γ′≤154° and here because Q′>1,61°≤3α′+β′+δ′+γ′≤154°. In this particular instance, in this embodimentof the cord 165 with a very low modulus, 65°≤3α′+β′+δ′+γ′≤153°, and herebecause Q′>1, 78°≤3α′+β′+δ′+γ′≤153°. In the case of the cord 165,3α′+β′+δ′+γ′=85.9°.

It will be noted that 84°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤280°. In this particularinstance, because Q=1 and Q′>1, 88°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤254°. In theembodiment of the cord 165 with a very low modulus,138°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤280° and because Q=1 and Q′>1,148°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤254°, and here 3α+β+δ+γ+3α′+β′+δ′+γ′=206.8°.

It will also be noted that 1.21≤EC/EI, preferably 1.21≤EC/EI≤3.00 andhere EC/EI=1.44.

Cord According to a 14^(th) Embodiment of the Invention

A medium-modulus cord 166 according to a seventh embodiment of theinvention will now be described. Elements similar to those of the cordsalready described are denoted by identical references.

Amongst the differences between the cords 160 and 166, it will be notedthat the helix angle α of each internal strand TI in the internal layerCI of the cord 166 ranges, in the embodiment of the cord 166 with amedium modulus, from 4° to 22°, in this instance α=17.9°. The helixangle α′ of each external strand TE in the external layer CE of the cord166 ranges, in the embodiment of the cord 166 with a medium modulus,from 11° to 21°, in this instance α′=13.2°.

It will also be noted that, in the first embodiment of the cord 166 witha medium modulus, 25°≤3α+β+δ+γ≤97°. In the case of the cord 166,3α+β+δ+γ=91°.

Also, in the case of the cord 166 with a medium modulus, 78 GPa≤EI≤180GPa, preferably 100 GPa≤EI≤180 GPa. Because the internal layer of thecord 166 has a relatively high modulus, 95 GPa≤EI≤180 GPa and here EI=96GPa.

It will also be noted that Q′>1, Q′=2, 3 or 4, P′=7, 8, 9 or 10, N′=13,14 or 15 and here Q′=3, P′=8 and N′=13. The Q′ internal threads F1′ arewound in a helix within each external strand TE at a pitch p1′ such that5 mm≤p1′≤15 mm. Here, p1′=12 mm. The helix angle β of each internalthread F1′ of the internal layer within each external strand TE rangesfrom 4° to 20°, here β′=4.5°. The P′ intermediate threads F2′ areassembled within each external strand TE at a pitch p2′ such that 10mm≤p2′≤20 mm. Here, p2′=18 mm. The helix angle δ′ of each intermediatethread F2′ in the intermediate layer C2′ within each external strand TEranges from 8° to 22°, here δ′=8.1°. The N′ external threads F3′ areassembled within each external strand TE at a pitch p3′ such that 10mm≤p3′≤40 mm. Here, p3′=25 mm. The helix angle γ′ of each externalthread F3′ in the external layer C3′ within each external strand TEranges from 9° to 25°, here γ′=9.6°.

It will also be noted that, in the case of the cord 166 with a mediummodulus, 48°≤3α′+β′+δ′+γ′≤89° and here because Q′>1,61°≤3α′+β′+δ′+γ′≤89° and here 3α′+β′+δ′+γ′=61.8°.

It is noted that, in the embodiment of the cord 166 with a mediummodulus, 84°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤161° and because Q=1 and Q′>1,88°≤3α+β+δ+γ+3α′+β′+δ′+γ′≤153° and here 3α+β+δ+γ+3α′+β′+δ′+γ′=152.8°.

Also, 1.21≤EC/EI, preferably 1.21≤EC/EI≤3.00 and here EC/EI=1.48.

Also, in this embodiment of the cord 166 with a medium modulus, 131GPa≤EC≤160 GPa. Here, EC=141 GPa.

Cord According to a 15^(th) Embodiment of the Invention

FIG. 9 depicts the low-modulus cord 260 according to a fifteenthembodiment of the invention.

The cord 260 is metal and of the multi-strand type with two cylindricallayers. Thus, it will be understood that there are two layers, not more,not less, of strands of which the cord 260 is made. The layers ofstrands are adjacent and concentric. The cord 260 is devoid of polymercompound and of elastomer compound when it is not integrated into thetyre.

The cord 260 comprises an internal layer CI of the cord 260, and anexternal layer CE of the cord 260. The internal layer CI is made up ofJ>1 internal strands TI, namely of several internal strands TI, wound ina helix. The external layer CE is made up of L>1 external strands,namely of several external strands TE wound in a helix around theinternal layer CI. In this instance, J=2, 3 or 4, preferably J=3 or 4.In addition, L=7, 8, 9 or 10, preferably L=8, 9 or 10. With J=3, L=7, 8or 9 and in this instance and here J=3, L=8.

The cord 260 also comprises a wrapper F made up of a single wrappingwire.

The internal layer CI is wound in a helix in a direction of winding ofthe internal layer of the cord, here the direction S. The internalstrands TI are wound in a helix with a pitch PI such that 10 mm≤PI≤65 mmand preferably 10 mm≤PI≤45 mm. Here, PI=20 mm. The helix angle α of eachinternal strand TI in the internal layer CI of the cord 260 ranges from3° to 36° and, in the case of the cord 260 with a low modulus, from 3°to 31° and in this instance α=13.6°.

The external layer CE is wound in a helix around the internal layer CIin a direction of winding of the external layer of the cord that is theopposite of the direction of winding of the internal layer of the cord,here the direction Z. The external strands TE are wound in a helixaround the internal strand TI with a pitch PE such that 30 mm≤PE≤65 mmand preferably 30 mm≤PE≤60 mm. Here, PE=40 mm. The helix angle α′ ofeach external strand TE in the external layer CE of the cord 260 rangesfrom 10 to 34 and, in the case of the cord 260 with a low modulus, from10° to 31° and in this instance α′=19.1°.

The wrapper F is wound around the external layer CE in a direction ofwinding of the wrapper, here the opposite to the direction of winding ofthe external layer CE, in this instance in the S-direction. The wrappingwire is wound in a helix around the external strands TE with a pitch PFsuch that 2 mm≤PF≤10 mm and preferably 3 mm≤PF≤8 mm. Here, PF=5.1 mm.

The assembly made up of the internal CI and external CE layers, whichmeans to say the cord 260 without the wrapper F, has a diameter Dgreater than or equal to 4 mm, preferably greater than or equal to 4.5mm, and less than or equal to 7 mm, preferably less than or equal to 6.5mm. Here, D=6.03 mm.

The internal layer CI of internal strands TI has a diameter DI. Eachexternal strand TE has a diameter DE. In this case, DI=2.87 mm, DE=1.58mm.

The external layer CE of the cord 260 is desaturated and incompletelyunsaturated.

The mean inter-strand distance E separating two adjacent externalstrands TE is greater than or equal to 30 μm. Here, the meaninter-strand distance E separating two adjacent external strands TE issuch that E=43 μm. The sum SIE of the inter-thread distances E of theexternal layer CE is less than the diameter DE of the external strandsof the external layer CE. Here, the sum SIE=8×0.043=0.34 mm, which is avalue strictly less than DE=1.58 mm.

Internal Strands TI of the Cord 260

Each internal strand TI has two layers. Each internal strand TIcomprises, here is made up of, two layers, not more, not less.

Each internal strand TI comprises an internal layer C1 made up of Q≥1internal threads F1 and an external layer C2 made up of N>1 externalthreads F2 wound in a helix around and in contact with the internallayer C1.

Q=2, 3 or 4, preferably Q=3 or 4. N=7, 8, 9 or 10, preferably N=8, 9 or10. With Q=4, N=7, 8 or 9 and in this instance Q=4, N=9.

The internal layer C1 of each internal strand TI is wound in a helix ina direction of winding of the internal layer C1 of the internal strandTI that is identical to the direction of winding of the internal layerC1 of the cord, here in the S-direction. The Q internal threads F1 areassembled within each internal strand TI at a pitch p1 such that 5mm≤p1≤20 mm. Here, p1=7.7 mm. The helix angle β of each internal threadF1 in the internal layer C1 within each internal strand TI ranges from4° to 17°, here β=9.9°.

The external layer C2 of each internal strand TI is wound around and incontact with the internal layer C1 in a direction of winding of theexternal layer C2 of the internal strand TI that is identical to thedirection of winding of the internal layer C1 of the cord, here in theS-direction. The N external threads F2 are wound in a helix around the Qinternal threads F1 and are assembled within each internal strand TI ata pitch p2 such that 5 mm≤p2≤40 mm. Here, p2=15.4 mm. The helix angle γof each external thread F2 in the external layer C2 within each internalstrand TI ranges from 7° to 20°, here γ=11.8°.

16°≤2α+β+γ≤105° and because Q>1, 20°≤2α+β+γ≤105°. In this particularinstance, in the case of the cord 260 with a low modulus. 16°≤2α+β+γ≤86°and because Q>1, 19°≤2α+β+γ85° and here 2α+β+γ=48.9°.

Each internal F1 and external F2 thread of each internal strand TIrespectively has a diameter D1, D2. Each diameter of the internalthreads D1 and external threads D2 of each internal strand TI rangesfrom 0.15 mm to 0.60 mm, preferably from 0.20 mm to 0.50 mm, morepreferentially from 0.23 mm to 0.45 mm and more preferentially stillfrom 0.25 mm to 0.40 mm. Each internal thread F1 of each internal strandTI has a diameter D1 greater than or equal to, here equal to, thediameter D2 of each external thread F2 of each internal strand TI. Inthis instance, D1=D2=0.30 mm.

Because of the relatively short pitch p2, the external layer C2 of eachinternal strand TI is desaturated and completely unsaturated. Theinter-thread distance I2 of the external layer C2 which on averageseparates the N external threads is greater than or equal to 5 μm. Theinter-thread distance I2 is preferably greater than or equal to 15 μm,more preferentially greater than or equal to 35 μm and here equal to 46μm. The sum SI2 of the inter-thread distances I2 of the external layerC2 is greater than the diameter d2 of the external threads F2 of theexternal layer C2. Here, the sum SI2=9×0.046=0.41 mm, which is a valuestrictly greater than D2=0.30 mm.

Also, 25 GPa≤EI≤180 GPa, preferably 36 GPa≤EI≤180 GPa and in the case ofthe cord 260 with a low modulus which has an internal layer with arelatively high modulus, 95 GPa≤EI≤180 GPa. In this instance, EI=148GPa.

External Strands TE of the Cord 260

Each external strand TE has three layers. Thus, each external strand TEcomprises, here is made up of, three layers, not more, not less.

Each external strand TE comprises an internal layer C′ made up of Q′>1internal threads F1′, an intermediate layer C2′ made up of P’>1intermediate threads F2′ wound in a helix around and in contact with theinternal layer C1′, and an external layer C3′ made up of N′>1 externalthreads F3′ wound in a helix around and in contact with the intermediatelayer C2′.

Q′=1, P′=5 or 6 and N′=10, 11 or 12, preferably Q′=1, P′=5 or 6, N′=10or 11 and more preferentially here Q′=1, P′=6 and N′=11.

In the instance in which Q′>1, the internal layer C1′ of each externalstrand TE is wound in a helix in a direction of winding of the internallayer C1′ of the external strand TE, the direction of winding of theinternal layer C1′ of the external strand TE is identical to thedirection of winding of the external layer CE of the cord, here in theZ-direction. Here, the Q′=1 internal thread F1′ is assembled within eachexternal strand TE at an infinite pitch p1′ such that β′=0.

The intermediate layer C2′ of each external strand TE is wound aroundand in contact with the internal layer C1′ in a direction of winding ofthe intermediate layer C2′ of the external strand TE that is identicalto the direction of winding of the external layer CE of the cord, herein the Z-direction. The P′ intermediate threads F2′ are wound in a helixaround the Q′=1 internal thread F1′ and are assembled within eachexternal strand TE at a pitch p2′ such that 5 mm≤p2′≤20 mm. Here,p2′=7.7 mm. The helix angle δ′ of each intermediate thread F2′ in theintermediate layer C2′ within each external strand TE ranges from 6° to22°, here γ′=15.5°.

The external layer C3′ of each external strand TE is wound around and incontact with the intermediate layer C2′ in a direction of winding of theexternal layer C3′ of the external strand TE that is identical to thedirection of winding of the external layer CE of the cord, here in theZ-direction. The N′ external threads F3′ are wound in a helix around theP′ intermediate threads F2′ and are assembled within each externalstrand TE at a pitch p3′ such that 10 mm≤p3′≤40 mm. Here, p3′=15.4 mm.The helix angle γ′ of each external thread F3′ in the external layer C3′within each external strand TE ranges from 7° to 22°, here γ′=14.6°.

47°≤3α′+β′+δ′+γ′≤147° and in the case of the cord 260 with a lowmodulus, 54°≤3α′+β′+δ′+γ′≤125° and because Q′=1, 54≤3α′+β′+δ′+γ′≤120°.In this particular instance, 3α′+β′+δ′+γ′=87.4°.

Each internal F1′, intermediate F2′ and external F3′ thread of eachexternal strand TE respectively has a diameter D1′, D2′, D3′. Eachdiameter of the internal threads D1′, intermediate threads D2′ andexternal threads D3′ of each external strand TE ranges from 0.15 mm to0.60 mm, preferably from 0.20 mm to 0.50 mm, more preferentially from0.23 mm to 0.45 mm and more preferentially still from 0.25 mm to 0.40mm. Each Q′ internal thread F1′ of each external strand TI′ has adiameter D1′ greater than or equal to the diameter D2′ of eachintermediate thread F2′ of each external strand TE. Each Q′ internalthread F1′ of each external strand TE has a diameter D1′ greater than orequal to the diameter D3′ of each external thread F3′ of each externalstrand TE. Each N′ intermediate thread F2′ of each external strand TEhas a diameter D2′ equal to the diameter D3′ of each external thread F3′of each external strand TE. In this instance, D1′=0.38 mm>D2′=D3′=0.30mm.

The intermediate layer C2′ of each external strand TE is desaturated andincompletely unsaturated. The inter-thread distance I2′ of theintermediate layer C2′ which on average separates the P′ intermediatethreads is greater than or equal to 5 μm. The inter-thread distance I2′is preferably greater than or equal to 15 μm and is here equal to 32 μm.The sum SI2′ of the inter-thread distances I2′ of the intermediate layerC2′ is greater than the diameter D2 of the intermediate threads F2′ ofthe intermediate layer C2′. Here, the sum SI2′=6×0.032=0.19 mm, a valuestrictly less than D2′=0.30 mm. In addition, the sum SI2′ of theinter-thread distances I2′ is such that SI2′<D3′ and even SI2′<0.8×D3′.

The external layer C3′ of each external strand TE is desaturated andcompletely unsaturated. The inter-thread distance I3′ of the externallayer C3′ which on average separates the N′ external threads is greaterthan or equal to 5 μm. The inter-thread distance I3′ is preferablygreater than or equal to 15 μm, more preferentially greater than orequal to 35 μm, more preferentially still greater than or equal to 50μm, and here is equal to 52 μm. The sum SI3′ of the inter-threaddistances I3′ of the external layer C3′ is greater than the diameter D3′of the external threads F3′ of the external layer C3′. Here, the sumSI3′=11×0.052=0.57 mm, which is a value strictly greater than D3′=0.30mm.

Each thread F1, F2, F1′, F2′, F3′ has a breaking strength, denoted Rm,such that 2500≤Rm≤3100 MPa. The steel for these threads is said to be ofSHT (“Super High Tensile”) grade. Other threads may be used, for examplethreads of an inferior grade, for example of NT (“Normal Tensile”) or HT(“High Tensile”) grade, just as may threads of a superior grade, forexample of UT (“Ultra Tensile”) or MT (“Mega Tensile”) grade.

84°≤2α+β+γ+3α′+β′+δ′+γ′≤226° and because Q>1 et Q′=1,88°≤2α+β+γ+3α′+β′+δ′+γ′≤206°. In the case of the cord 260 with a lowmodulus, 87°≤2α+β+γ+3α′+β′+δ′+γ′≤172° and because Q>1 and Q′=1,90°≤2α+β+γ+3α′+β′+δ′+γ′≤165°. In this instance2α+β+γ+3α′+β′+δ′+γ′=136.3°.

0.60≤EC/EI≤1.20 and here EC/EI=0.69.

Also, 50 GPa≤EC≤160 GPa and in this embodiment 90 GPa≤EC≤130 GPa. Here,EC=102 GPa.

Cord According to a 16^(th) Embodiment of the Invention

A low-modulus cord 261 according to a second embodiment of the inventionwill now be described. Elements similar to those of the cord 260 aredenoted by identical references.

Amongst the differences between the cords 260 and 261, it will be notedthat Q=1, N=5 or 6, and here Q=1, N=6.

It will also be noted that the N external threads F2 are wound in ahelix around the Q=1 internal thread F1 and are assembled within eachinternal strand TI at a pitch p2 such that 5 mm≤p2≤30 mm. Here, p2=7.7mm. The helix angle γ of each external thread F2 in the external layerC2 within each internal strand TI ranges from 5° to 26°, here γ=12.9°.

It will also be noted that 16°≤2α+β+γ≤105° and because Q=1,16°≤2α+β+γ≤86° and here 2α+β+γ=26.5°.

It will be noted that, because Q=1 and Q′=1,84°≤2α+β+γ+3α′+β′+δ′+γ′≤199°.

In the case of the cord 261 with a low modulus, with Q=1 and Q′=1,87°≤2α+β+γ+3α′+β′+δ′+γ′≤160°. In this instance2α+β+γ+3α′+β′+δ′+γ′=136.3°.

It will be noted that EC/EI≤0.59, and preferably 0.40≤EC/EI≤0.59 andhere EC/EI=0.56.

Cord According to a 17^(th) Embodiment of the Invention

A low-modulus cord 262 according to a third embodiment of the inventionwill now be described. Elements similar to those of the cords alreadydescribed are denoted by identical references.

Amongst the differences between the cords 260 and 262, it will be notedthat, because the internal layer of the cord 262 with a low modulus hasa relatively low modulus, 25 GPa≤EI≤94 GPa, preferably 64 GPa≤EI≤94 GPa.In this instance, EI=71 GPa.

It will be noted that 1.21≤EC/EI and preferably 1.21≤EC/EI≤3.00 and inthe case of the cord 262 with a low modulus, 1.21≤EC/EI≤2.82, and hereEC/EI=1.33.

Cord According to a 18^(th) Embodiment of the Invention

A very low-modulus cord 263 according to a fourth embodiment of theinvention will now be described. Elements similar to those of the cordsalready described are denoted by identical references.

Amongst the differences between the cords 260 and 263, it will be notedthat the helix angle α of each internal strand TI in the internal layerCI of the cord 263 ranges, in the case of the cord 263 with a very lowmodulus, from 5° to 36° and in this instance α=10°. It will also benoted that the helix angle α′ of each external strand TE in the externallayer CE of the cord 263 ranges, in the case of the cord 263 with a verylow modulus, from 14 to 34 and in this instance α′=14.5°.

It will also be noted that, in the case of the cord 263 with a very lowmodulus, 20°≤2α+β+γ≤105° and because Q>1, 27°≤2α+β+γ≤105° and here2α+β+γ=53.6°.

It will be noted that, in the case of the cord 263 with a very lowmodulus, 25 GPa≤EI≤180 GPa, preferably 36 GPa≤EI≤175 GPa. In the case ofthe cord 263 that has an internal layer with a relatively high modulus,95 GPa≤EI≤180 GPa, preferably 95 GPa≤EI≤175 GPa. In this instance,EI=130 GPa.

It will be noted that, in the case of the cord 263 with a very lowmodulus and because Q′=1, 66°≤3α′+β′+δ′+γ′≤147°. In this particularinstance, 3α′+β′+δ′+γ′=⁹³0.5°.

It will also be noted that, in the case of the cord 263 with a very lowmodulus, 146°≤2α+β+γ+3α′+β′+δ′+γ′≤226° and because Q>1 and Q′=1, 1300 S2α+β+γ+3α′+β′+δ′+γ′≤206°. In this instance 2α+β+γ+3α′+β′+δ′+γ′=147.1°.

In the case of the cord 263 with a very low modulus, 0.60≤EC/EI≤1.20 andhere EC/EI=0.64.

It will also be noted that, in this embodiment of the cord 263 with avery low modulus, 50 GPa≤EI 89 GPa. Here, EC=84 GPa.

Cord According to a 19^(th) Embodiment of the Invention

A very low-modulus cord 264 according to a fifth embodiment of theinvention will now be described. Elements similar to those of the cordsalready described are denoted by identical references.

Amongst the differences between the cords 263 and 264, it will be notedthat, in the case of the cord 264 with a very low modulus that has aninternal layer with a relatively low modulus, 25 GPa≤EI≤94 GPa,preferably 36 GPa≤EI≤94 GPa. In this instance, EI=42 GPa.

It will be noted that Q′>1, and here Q′=2, 3 or 4, P′=7, 8, 9 or 10,N′=13, 14 or 15 and here Q′=3, P′=8 and N′=13.

It will be noted that the Q′ internal threads F1′ are wound in a helixwithin each external strand TE at a pitch p1′ such that 5 mm≤p1′≤15 mm.Here, p1′=12 mm. The helix angle β of each internal thread F1′ of theinternal layer within each external strand TE ranges from 4° to 20°,here β′=6°. The P′ intermediate threads F2′ are assembled within eachexternal strand TE at a pitch p2′ such that 10 mm≤p2′≤20 mm. Here,p2′=18 mm. The helix angle δ′ of each intermediate thread F2′ in theintermediate layer C2′ within each external strand TE ranges from 8° to22°, here δ′=10.9°. The N′ external threads F3′ are assembled withineach external strand TE at a pitch p3′ such that 10 mm≤p3′≤40 mm. Here,p3′=25 mm. The helix angle γ′ of each external thread F3′ in theexternal layer C3′ within each external strand TE ranges from 9° to 25°,here γ′=12.8°.

It will also be noted that, in the case of the cord 264 with a very lowmodulus and because Q′>1, 75°≤3α′+β′+δ′+γ′≤140°. In this particularinstance, 3α′+β′+δ′+γ′=95.7°.

It will be noted that, in the case of the cord 264 with a very lowmodulus and because Q>1 and Q′>1, 146°≤2α+β+γ+3α′+β′+δ′+γ′≤226°. In thisparticular instance, 2α+β+γ+3α′+β′+δ′+γ′=188.9°.

It will be noted that, in the case of the cord 264 with a very lowmodulus, 1.21≤EC/EI and preferably 1.21≤EC/EI≤3.00 and here EC/EI=1.72.

Cord According to a 20^(th) Embodiment of the Invention

A medium-modulus cord 265 according to a sixth embodiment of theinvention will now be described. Elements similar to those of the cordsalready described are denoted by identical references.

Amongst the differences between the cords 260 and 265, it will be notedthat the helix angle α of each internal strand TI in the internal layerCI of the cord 265 with a medium modulus ranges from 3° to 20° and inthis instance α=6.8°. It will also be noted that the helix angle α′ ofeach external strand TE in the external layer CE of the cord 265 with amedium modulus ranges from 100 to 220 and in this instance α′=15.3°.

It will also be noted that Q=1, N=5 or 6 and here Q=1, N=6. The Nexternal threads F2 are wound in a helix around the Q=1 internal threadF1 and are assembled within each internal strand TI at a pitch p2 suchthat 5 mm≤p2≤30 mm. Here, p2=5 mm. The helix angle γ of each externalthread F2 in the external layer C2 within each internal strand TI rangesfrom 5° to 26°, here γ=19.4°.

It will be noted that, in the case of the cord 265 with a mediummodulus, 16°≤2α+β+γ≤68° and because Q=1, 16°≤2α+β+γ≤56° and here2α+β+γ=33°.

It will also be noted that, in the case of the cord 265 with a mediummodulus, 78 GPa≤EI≤180 GPa, preferably 100 GPa≤EI≤180 GPa, and in thecase of the cord 265 that has an internal layer with a relatively highmodulus, 95 GPa≤EI≤180 GPa and, in this instance, EI=165 GPa.

It will be noted that, in the case of the cord 265 with a mediummodulus, 47°≤3α′+β′+δ′+γ′≤89° and because Q′=1, 47°≤3α′+β′+δ′+γ′≤86°. Inthis particular instance, 3α′+β′+δ′+γ′=71.4°.

It will be noted that, in the case of the cord 265 with a mediummodulus, 84°≤2α+β+γ+3α′+β′+δ′+γ′≤136°, and because Q=1 and Q′=1,84°≤2α+β+γ+3α′+β′+δ′+γ′≤112°. In this particular instance,2α+β+γ+3α′+β′+δ′+γ′=104.2°.

It will also be noted that, in the case of the cord 265 with a mediummodulus, in the case of the cord 265 with a medium modulus,0.60≤EC/EI≤1.20, preferably 0.80≤EC/EI≤1.15 and here EC/EI=0.90.

Also, 50 GPa≤EC≤160 GPa and in the embodiment of the cord 265 with amedium modulus, 131 GPa≤EC≤160 GPa. Here, EC=148 GPa.

Cord According to a 21^(st) Embodiment of the Invention

A medium-modulus cord 266 according to a seventh embodiment of theinvention will now be described. Elements similar to those of the cordsalready described are denoted by identical references.

Amongst the differences between the cords 265 and 266, it will be notedthat Q=2, 3 or 4, preferably Q=3 or 4. N=7, 8, 9 or 10. With Q=3 andN=7, 8 or 9 and here Q=3, N=8.

It will be noted that the Q internal threads F1 are assembled withineach internal strand TI at a pitch p1 such that 5 mm≤p1≤20 mm. Here,p1=12 mm. The helix angle β of each internal thread F1 in the internallayer C1 within each internal strand TI ranges from 4° to 17°, hereβ=6°. The N external threads F2 are wound in a helix around the Qinternal threads F1 and are assembled within each internal strand TI ata pitch p2 such that 5 mm≤p2≤40 mm. Here, p2=18 mm. The helix angle γ ofeach external thread F2 in the external layer C2 within each internalstrand TI ranges from 7° to 20°, here γ=10.9°.

It will be noted that, in the case of the cord 266 with a mediummodulus, because Q>1, 20°≤2α+β+γ≤68° and here 2α+β+γ=26.9°.

It will also be noted that Q′>1, and here Q′=2, 3 or 4, P′=7, 8, 9 or10, N′=13, 14 or 15 and here Q′=3, P′=8 and N′=13.

It will be noted that the Q′ internal threads F1′ are wound in a helixwithin each external strand TE at a pitch p1′ such that 5 mm≤p1′≤15 mm.Here, p1′=12 mm. The helix angle β of each external thread F1′ of theinternal layer within each external strand TE ranges from 4° to 20°,here β′=4.5°. The P′ intermediate threads F2′ are assembled within eachexternal strand TE at a pitch p2′ such that 10 mm≤p2′≤20 mm. Here,p2′=18 mm. The helix angle δ′ of each intermediate thread F2′ in theintermediate layer C2′ within each external strand TE ranges from 8° to22°, here δ′=8.1°. The N′ external threads F3′ are assembled within eachexternal strand TE at a pitch p3′ such that 10 mm≤p3′≤40 mm. Here,p3′=25 mm. The helix angle γ′ of each external thread F3′ in theexternal layer C3′ within each external strand TE ranges from 9° to 25°,here γ′=9.6°.

It will be noted that, in the case of the cord 266 with a medium modulusand because Q′>1, 620≤3α′+β′+δ′+γ≤89° and here 3α′+β′+δ′+γ′=77.1°.

Cord According to a 22^(nd) Embodiment of the Invention

FIG. 10 depicts the cord 360 according to a sixth embodiment of theinvention.

The cord 360 is metal and is of the multi-strand type with twocylindrical layers. Thus, it will be understood that there are twolayers, not more, not less, of strands of which the cord 360 is made.The layers of strands are adjacent and concentric. The cord 360 isdevoid of polymer compound and of elastomer compound when it is notintegrated into the tyre.

The cord 360 comprises an internal layer CI of the cord 360, and anexternal layer CE of the cord 360. The internal layer CI is made up ofJ>1 internal strands TI, namely of several internal strands TI, wound ina helix. The external layer CE is made up of L>1 external strands,namely of several external strands TE wound in a helix around theinternal layer CI. In this instance, J=2, 3 or 4, preferably J=3 or 4.In addition, L=7, 8, 9 or 10, preferably L=8, 9 or 10. With J=3, L=7, 8or 9 and in this instance and here J=3, L=8.

The cord 360 also comprises a wrapper F made up of a single wrappingwire.

The internal layer CI is wound in a helix in a direction of winding ofthe internal layer of the cord, here the direction S. The internalstrands TI are wound in a helix with a pitch PI such that 10 mm≤PI≤65 mmand preferably 10 mm≤PI≤45 mm. Here, PI=20 mm. The helix angle α of eachinternal strand TI in the internal layer CI of the cord 360 ranges from4° to 36° and in the embodiment of the cord 360 with a low modulus from4° to 27° and in this instance α=13.4°.

The external layer CE is wound in a helix around the internal layer CIin a direction of winding of the external layer of the cord that is theopposite of the direction of winding of the internal layer of the cord,here the direction Z. The external strands TE are wound in a helixaround the internal strand TI with a pitch PE such that 30 mm≤PE≤65 mmand preferably 30 mm≤PE≤60 mm. Here, PE=40 mm. The helix angle α′ ofeach external strand TE in the external layer CE of the cord 360 rangesfrom 10° to 32° and, in the embodiment of the cord 360 with a lowmodulus, from 11° to 31° and in this instance α′=18.6°.

The wrapper F is wound around the external layer CE in a direction ofwinding of the wrapper, here the opposite to the direction of winding ofthe external layer CE, in this instance in the S-direction. The wrappingwire is wound in a helix around the external strands TE with a pitch PFsuch that 2 mm≤PF≤10 mm and preferably 3 mm≤PF≤8 mm. Here, PF=5.1 mm.

The assembly made up of the internal CI and external CE layers, whichmeans to say the cord 360 without the wrapper F, has a diameter Dgreater than or equal to 4 mm, preferably greater than or equal to 4.5mm, and less than or equal to 7 mm, preferably less than or equal to 6.5mm. Here, D=5.7 mm.

The internal layer CI of internal strands TI has a diameter DI. Eachexternal strand TE has a diameter DE. In this case, DI=2.83 mm, DE=1.46mm.

The external layer CE of the cord 360 is desaturated and incompletelyunsaturated. The mean inter-strand distance E separating two adjacentexternal strands TE is greater than or equal to 30 μm, preferablygreater than or equal to 70 μm and more preferentially greater than orequal to 100 μm. Here, the mean inter-strand distance E separating twoadjacent external strands TE is such that E=117 μm. The sum SIE of theinter-thread distances E of the external layer CE is less than thediameter DE of the external strands of the external layer CE. Here, thesum SIE=8×0.117=0.94 mm, which is a value strictly less than DE=1.46 mm.

Internal Strands TI of the Cord 360

Each internal strand TI has three layers. Each internal strand TIcomprises, here is made up of, three layers, not more, not less.

Each internal strand TI comprises an internal layer C1 made up of Q>1internal threads F1, an intermediate layer C2 made up of P>1intermediate threads F2 wound in a helix around and in contact with theinternal layer C1, and an external layer C3 made up of N>1 externalthreads F3 wound in a helix around and in contact with the intermediatelayer C2.

Q=1, P=5 or 6 and N=10, 11 or 12, preferably Q=1, P=5 or 6, N=10 or 11and more preferentially here Q=1, P=6 and N=11.

In the instance in which Q>1, the internal layer C1 of each internalstrand TI is wound in a helix in a direction of winding of the internallayer C1 of the internal strand TI that is identical to the direction ofwinding of the internal layer C1 of the cord, here in the S-direction.Here, the Q=1 internal thread F1 is assembled within each internalstrand TI at an infinite pitch such that β=0.

The intermediate layer C2 of each internal strand TI is wound around andin contact with the internal layer C1 in a direction of winding of theintermediate layer C2 of the internal strand TI that is identical to thedirection of winding of the internal layer CI of the cord, here in theS-direction. The P intermediate threads F2 are wound in a helix aroundthe Q=1 internal thread F1 and are assembled within each internal strandTI at a pitch p2 such that 5 mm≤p2≤20 mm. Here, p2=7.7 mm. The helixangle δ of each intermediate thread F2 in the intermediate layer C2within each internal strand TI ranges from 6° to 30°, here δ=12.2°.

The external layer C3 of each internal strand TI is wound around and incontact with the intermediate layer C2 in a direction of winding of theexternal layer C3 of the internal strand TI that is identical to thedirection of winding of the internal layer CI of the cord, here in theS-direction. The N external threads F3 are wound in a helix around the Pintermediate threads F2 and are assembled within each internal strand TIat a pitch p3 such that 10 mm≤p3≤40 mm. Here, p3=15.4 mm. The helixangle γ of each external thread F3 in the external layer C3 within eachinternal strand TI ranges from 7° to 30°, here γ=12.1°.

26°≤3α+β+δ+γ≤162° and here because Q=1, 26°≤3α+β+δ+γ≤140°. In thisparticular instance, in this first embodiment of the cord 360 with a lowmodulus, 26°≤3α+β+δ+γ≤128° and here because Q>1, 26°≤3α+β+γ+γ≤113°. Inthe case of the cord 360, 3α+β+δ+γ=64.5°.

Each internal F1, intermediate F2 and external F3 thread of eachinternal strand TI respectively has a diameter D1, D2, D3. Each diameterof the internal threads D1, intermediate threads D2 and external threadsD3 of each internal strand TI ranges from 0.15 mm to 0.60 mm, preferablyfrom 0.20 mm to 0.50 mm, more preferentially from 0.23 mm to 0.45 mm andmore preferentially still from 0.25 mm to 0.40 mm. Each internal threadF1 of each internal strand TI has a diameter D1 greater than or equalto, here equal to, the diameter D2 of each intermediate thread F2 ofeach internal strand TI. Each internal thread F1 of each internal strandTI has a diameter D1 greater than or equal to, here equal to, thediameter D3 of each external thread F3 of each internal strand TI. Eachintermediate thread F2 of each internal strand TI has a diameter D2equal to the diameter D3 of each external thread F3 of each internalstrand TI. In this instance, D1=D2=D3=0.26 mm.

The intermediate layer C2 of each internal strand TI is saturated. Here,the distance I2 is approximately equal to 0.

The external layer C3 of each internal strand TI is desaturated andcompletely unsaturated. The inter-thread distance I3 of the externallayer C3 which on average separates the N external threads is greaterthan or equal to 5 μm. The inter-thread distance I3 is preferablygreater than or equal to 15 μm and is here equal to 30 μm. The sum SI3of the inter-thread distances I3 of the external layer C3 is greaterthan the diameter D3 of the external threads F3 of the external layerC3. Here, the sum SI3=11×0.030=0.33 mm, which is a value strictlygreater than D2=0.26 mm.

Also, 25 GPa≤EI≤180 GPa, preferably 36 GPa≤EI≤180 GPa. In the case ofthe cord 360 with a low modulus, 25 GPa≤EI≤180 GPa, preferably 36GPa≤EI≤175 GPa. Here, the internal layer has a relatively high modulus,so 95 GPa≤EI≤180 GPa. In this instance, EI=147 GPa.

External Strands TE of the Cord 360

Each external strand TE has two layers. Thus, each external strand TEcomprises, here is made up of, two layers, not more, not less.

Each external strand TE comprises an internal layer C1′ made up of Q′≥1internal threads F1′ and an external layer C2′ made up of N′>1 externalthreads F2′ wound in a helix around and in contact with the internallayer C1′.

Q′=2, 3 or 4, preferably Q′=3 or 4. N′=7, 8, 9 or 10, preferably N′=8, 9or 10. With Q′=3, N′=7, 8 or 9 and in this instance Q′=3, N′=8.

The internal layer C1′ of each external strand TE is wound in a helix ina direction of winding of the internal layer C1′ of the external strandTE that is identical to the direction of winding of the external layerCE of the cord, here in the Z-direction. The Q′ internal threads F1′ areassembled within each external strand TE at a pitch p1′ such that 5mm≤p1′≤20 mm. Here, p1′=7.7 mm. The helix angle β of each internalthread F1′ in the internal layer C1′ within each external strand TEranges from 4° to 17°, here β′=9.4°.

The external layer C2′ of each external strand TE is wound around and incontact with the internal layer C1′ in a direction of winding of theexternal layer C2′ of the internal strand TE that is identical to thedirection of winding of the external layer CE of the cord, here in theZ-direction. The N′ external threads F2′ are wound in a helix around theQ′ internal threads F1′ and are assembled within each external strand TEat a pitch p2′ such that 5 mm≤p2′≤40 mm. Here, p2′=15.4 mm. The helixangle γ′ of each external thread F2′ in the external layer C2′ withineach external strand TE ranges from 7° to 20°, here γ′=12.7°.

28°≤2α′+β′+γ′≤960 and here because Q′>1, 34°≤2α′+β′+γ′≤96°. In thisparticular instance, in this first embodiment of the cord 360 with a lowmodulus, 28°≤2α′+′+γ′≤89 and here because Q′=1, 36°≤2α′+β′+γ′≤89°. Inthe case of the cord 360, 2α′+β+γ′=59.3°.

Each internal F1′ and external F2′ thread of each external strand TErespectively has a diameter D1′, D2′. Each diameter of the internalthreads D1′ and external threads D2′ of each external strand TE rangesfrom 0.15 mm to 0.60 mm, preferably from 0.20 mm to 0.50 mm, morepreferentially from 0.23 mm to 0.45 mm and more preferentially stillfrom 0.25 mm to 0.40 mm. Each Q′ internal thread F1′ of each externalstrand TI′ has a diameter D1′ greater than or equal to, here equal to,the diameter D2′ of each external thread F2′ of each external strand TE.In this instance, D1′=D2′=0.35 mm.

The external layer C2′ of each external strand TE is desaturated andcompletely unsaturated. The inter-thread distance I2′ of the externallayer C2′ which on average separates the N′ external threads is greaterthan or equal to 5 μm. The inter-thread distance I2′ is preferablygreater than or equal to 15 μm, more preferentially greater than orequal to 35 μm, more preferentially still greater than or equal to 50 μmand highly preferentially greater than or equal to 60 μm and is hereequal to 66 μm. The sum SI2′ of the inter-thread distances I2′ of theexternal layer C2′ is greater than the diameter D2′ of the externalthreads F2′ of the external layer C2′. Here, the sum SI2′=8×0.066=0.53mm, which is a value strictly greater than D2′=0.35 mm.

Each thread F1, F2, F3, F1′, F2′ has a breaking strength, denoted Rm,such that 2500≤Rm≤3100 MPa. The steel for these threads is said to be ofSHT (“Super High Tensile”) grade. Other threads may be used, for examplethreads of an inferior grade, for example of NT (“Normal Tensile”) or HT(“High Tensile”) grade, just as may threads of a superior grade, forexample of UT (“Ultra Tensile”) or MT (“Mega Tensile”) grade.

64°≤3α+β+γ+γ+2α′+β′+γ′≤224°. In this particular instance, because Q=1and Q′>1, 68°≤3α+β+δ+γ+2α′+β′+γ′≤220°. In the embodiment of the cord 360with a low modulus, 74°≤3α+β+δ+γ+2α′+β′+γ′≤183° and, because Q=1 andQ′>1, 84°≤3α+β+δ+γ+2α′+β′+γ′≤168° and here 3α+β+δ+γ+2α′+β′+γ′=123.8°.

0.60≤EC/EI≤1.20 and here EC/EI=0.75.

Also, 50 GPa≤EC≤160 GPa and in this embodiment of the cord 360 with alow modulus, 90 GPa≤EC≤130 GPa. Here, EC=111 GPa.

Cord According to a 23^(th) Embodiment of the Invention

A low-modulus cord 361 according to a second embodiment of the inventionwill now be described. Elements similar to those of the cord 360 aredenoted by identical references.

Amongst the differences between the cords 360 and 361, it will beparticularly noted that Q>1, Q=2, 3 or 4, P=7, 8, 9 or 10, N=13, 14 or15 and here Q=3, P=8 and N=13.

It will be noted that the Q internal threads F1 are wound in a helixwithin each internal strand TI at a pitch p1 such that 5 mm≤p1≤15 mm.Here, p1=12 mm. The helix angle β of each internal thread F1 of theinternal layer within each internal strand TI ranges from 4° to 17°,here β=6°. The P intermediate threads F2 are wound in a helix around theQ internal threads F1 and are assembled within each internal strand TIat a pitch p2 such that 10 mm≤p2≤20 mm. Here, p2=18 mm. The helix angleδ of each intermediate thread F2 in the intermediate layer C2 withineach internal strand TI ranges from 8° to 22°, here δ=10.9°. The Nexternal threads F3 are wound in a helix around the P intermediatethreads F2 and are assembled within each internal strand TI at a pitchp3 such that 10 mm≤p3≤40 mm. Here, p3=25 mm. The helix angle γ of eachexternal thread F3 in the external layer C3 within each internal strandTI ranges from 9° to 25° here γ=12.8°.

It will also be noted that, because Q>1, 36°≤3α+β+δ+γ≤162°. In thisparticular instance, in this embodiment of the cord 361 with a lowmodulus and because Q>1, 36°≤3α+β+δ+γ128° and here 3α+β+δ+γ=51.9°.

It will be noted that Q′=1 and here, N′=5 or 6, preferably N′=6.

It will be noted that the N′ external threads F2′ are wound in a helixaround the Q′ internal threads F1′ and are assembled within eachexternal strand TE at a pitch p2′ such that 5 mm≤p2′≤30 mm. Here, p2′=15mm. The helix angle γ′ of each external thread F2′ in the external layerC2′ within each external strand TE ranges from 5° to 26°, here γ′=8.8°.

It will be noted that, because Q′>1, 28°≤2α′+β′+γ′≤86°. In thisparticular instance, in this embodiment of the cord 361 with a lowmodulus, 28°≤2α′+β′+γ′≤85°. In the case of the cord 361,2α′+β′+γ′=63.4°.

It will be noted that, because Q>1 and Q′=1,73°≤3α+β+δ+γ+2α′+β′+γ′≤212°.

In the embodiment of the cord 361 with a low modulus,86°≤3α+β+δ+γ+2α′+β′+γ′≤168° and here 3α+β+δ+γ+2α′+β′+γ′=115.3°.

Cord According to a 24^(th) Embodiment of the Invention

A low-modulus cord 362 according to a third embodiment of the inventionwill now be described. Elements similar to those of the cords alreadydescribed are denoted by identical references.

Amongst the differences between the cords 360 and 362, it will be notedthat 28 GPa≤EI≤94 GPa and, in the case of the cord 362 with a lowmodulus that has an internal layer with a relatively low modulus, 25GPa≤EI≤94 GPa, preferably 64 GPa≤EI 94 GPa. In this instance, EI=65 GPa.

It will also be noted that Q′=1, N′=5 or 6 and here preferably N′=6. TheN′ external threads F2′ are wound in a helix around the Q′=1 internalthread F1′ and are assembled within each external strand TE at a pitchp2′ such that 5 mm≤p2′≤30 mm. Here, p2′=15 mm. The helix angle γ′ ofeach external thread F2′ in the external layer C2′ within each externalstrand TE ranges from 5° to 26°, here γ′=8.8°.

It will be noted that, because Q′=1, 28°≤2α′+β′+γ′≤86° and, in thisembodiment of the cord 362 with a low modulus, 28°≤2α′+β′+γ′≤85°. In thecase of the cord 362, 2α′+β′+γ′=36.4°.

It will also be noted that, because Q=1 and Q′=1,64°≤3α+β+δ+γ+2α′+β′+Y'S 200°, and in the embodiment of the cord 362 witha low modulus, 74°≤3α+β+δ+γ+2α′+β′+γ′≤158° and here3α+β+δ+γ+2α′+β′+γ′=148.5°.

Also, 1.21≤EC/EI, and preferably 1.21≤EC/EI≤3.00 and in the embodimentof the cord 362 with a low modulus, 1.21≤EC/EI≤2.82, and hereEC/EI=1.54.

Cord According to a 25^(th) Embodiment of the Invention

A very low-modulus cord 363 according to a fourth embodiment of theinvention will now be described. Elements similar to those of the cordsalready described are denoted by identical references.

Amongst the differences between the cords 360 and 363, it will be notedthat the helix angle α of each internal strand TI in the internal layerCI of the cord 363 with a very low modulus ranges from 4° to 36° and inthis instance α=26.7°. It will be noted that the helix angle α′ of eachexternal strand TE in the external layer CE of the cord 363 with a verylow modulus ranges from 130 to 320 and in this instance α′=16°.

It will be noted that Q>1, Q=2, 3 or 4, P=7, 8, 9 or 10, N=13, 14 or 15and here Q=3, P=8 and N=13. The Q internal threads F1 are wound in ahelix within each internal strand TI at a pitch p1 such that 5 mm≤p1≤15mm. Here, p1=5 mm. The helix angle β of each internal thread F1 of theinternal layer within each internal strand TI ranges from 4° to 17°,here β=10.7°. The P intermediate threads F2 are wound in a helix aroundthe Q internal threads F1 and are assembled within each internal strandTI at a pitch p2 such that 10 mm≤p2≤20 mm. Here, p2=10 mm. The helixangle δ of each intermediate thread F2 in the intermediate layer C2within each internal strand TI ranges from 8° to 22°, here δ=14.5°. TheN external threads F3 are wound in a helix around the P intermediatethreads F2 and are assembled within each internal strand TI at a pitchp3 such that 10 mm≤p3≤40 mm. Here, p3=15 mm. The helix angle γ of eachexternal thread F3 in the external layer C3 within each internal strandTI ranges from 9° to 25°, here γ=15.7°.

It will be noted that, in this embodiment of the cord 363 with a verylow modulus, 35≤3α+β+δ+γ≤162° and here because Q>1, 36°≤3α+β+γ+γ≤162°.In the case of the cord 363, 3α+β+δ+γ=121°.

It will also be noted that, in the case of the cord 363 having a verylow modulus, 25 GPa≤EI≤180 GPa, preferably 36 GPa≤EI≤175 GPa and,because the internal layer has a relatively low modulus, 25 GPa≤EI≤94GPa, preferably 36 GPa≤EI≤94 GPa. In this instance, EI=73 GPa.

It will be noted that, in the case of the cord 363 with a very lowmodulus, 34≤2α′+β′+γ′≤96° and here because Q′>1, 42°≤2α′+β′+γ′≤96 andhere, 2α′+β′+γ′=65.6°.

It will also be noted that, in the case of the cord 363 with a very lowmodulus, 10°≤3α+β+δ+γ+2α′+3′+γ′≤224° and, because Q>1 and Q′=1,121°≤3α+β+δ+γ+2α′+β′+γ′≤224° and here 3α+β+δ+γ+2α′+β′+γ′=186.6°.

It will be noted that, in the case of the cord 363 with a very lowmodulus, 0.60≤EC/EI≤1.20 and here EC/EI=1.14.

Also, 50 GPa≤EC≤160 GPa and in this embodiment of the cord 363 with avery low modulus, 50 GPa≤EC≤89 GPa. Here, EC=83 GPa.

Cord According to a 26^(th) Embodiment of the Invention

A very low-modulus cord 364 according to a fifth embodiment of theinvention will now be described. Elements similar to those of the cordsalready described are denoted by identical references.

Amongst the differences between the cords 363 and 364, it will be notedthat Q=1, P=5 or 6 and N=10, 11 or 12, preferably Q=1, P=5 or 6, N=10 or11 and here, more preferentially Q=1, P=6 and N=11. The P intermediatethreads F2 are wound in a helix around the Q=1 internal thread F1 andare assembled within each internal strand TI at a pitch p2 such that 5mm≤p2≤20 mm. Here, p2=5 mm. The helix angle δ of each intermediatethread F2 in the intermediate layer C2 within each internal strand TIranges from 6° to 30°, here δ=19.4°. The N external threads F3 are woundin a helix around the P intermediate threads F2 and are assembled withineach internal strand TI at a pitch p3 such that 10 mm≤p3≤40 mm. Here,p3=10 mm. The helix angle γ of each external thread F3 in the externallayer C3 within each internal strand TI ranges from 7° to 30°, hereγ=18.7°.

It will be noted that, because Q=1, in the embodiment of the cord 364with a very low modulus, 35°≤3α+β+δ+γ≤140° and here, 3α+β+δ+γ≤51.9°.

It will be noted that, because the cord 364 with a very low modulus hasan internal layer of the cord with a relatively high modulus, 95GPa≤EI≤180 GPa, preferably 95 GPa≤EI≤175 GPa. In this instance, EI=146GPa.

It will also be noted that Q′=1 and here, N′=5 or 6, preferably N′=6.The N′ external threads F2′ are wound in a helix around the Q′=1internal thread F1′ and are assembled within each external strand TE ata pitch p2′ such that 5 mm≤p2′≤30 mm. Here, p2′=5 mm. The helix angle γ′of each external thread F2′ in the external layer C2′ within eachexternal strand TE ranges from 5° to 26°, here γ′=25.4°.

It will be noted that, because Q′=1, 28°≤2α′+β′+γ′≤86 and in thisembodiment of the cord 364 with a very low modulus, 34°≤2α′+β′+γ′≤86°and here 2α′+β′+γ′=64.8°.

It will also be noted that, because Q=1 and Q′=1,64°≤3α+β+δ+γ+2α′+β′+γ′≤200° and in the embodiment of the cord 364 with avery low modulus, 100°≤3α+β+δ+γ+2α′+β′+γ′≤200° and here3α+β+δ+γ+2α′+β′+γ′=116.7°.

It will also be noted that EC/EI≤0.59 and here EC/EI=0.58.

Cord According to a 27^(th) Embodiment of the Invention

A medium-modulus cord 365 according to a sixth embodiment of theinvention will now be described. Elements similar to those of the cordsalready described are denoted by identical references.

Amongst the differences between the cords 360 and 365, it will be notedthat the helix angle α of each internal strand TI in the internal layerCI ranges, in the case of the cord with a medium modulus 65, from 4° to23° and in this instance α=11°. The helix angle α′ of each externalstrand TE in the external layer CE ranges, in the case of the cord witha medium modulus 65, from 10° to 27° and in this instance α′=17°.

It will also be noted that Q>1, Q=2, 3 or 4, P=7, 8, 9 or 10, N=13, 14or 15 and here Q=3, P=8 and N=13. The Q internal threads F1 are wound ina helix within each internal strand TI at a pitch p1 such that 5mm≤p1≤15 mm. Here, p1=8 mm. The helix angle β of each internal thread F1of the internal layer within each internal strand TI ranges from 4° to17°, here β=6.7°. The P intermediate threads F2 are wound in a helixaround the Q internal threads F1 and are assembled within each internalstrand TI at a pitch p2 such that 10 mm≤p2≤20 mm. Here, p2=15 mm. Thehelix angle δ of each intermediate thread F2 in the intermediate layerC2 within each internal strand TI ranges from 8° to 22°, here δ=9.8°.The N external threads F3 are wound in a helix around the P intermediatethreads F2 and are assembled within each internal strand TI at a pitchp3 such that 10 mm≤p3≤40 mm. Here, p3=20 mm. The helix angle γ of eachexternal thread F3 in the external layer C3 within each internal strandTI ranges from 9° to 25°, here γ=11.9°.

It will also be noted that, in the case of the cord 365 with a mediummodulus and because Q>1, 26°≤3α+β+δ+γ≤97° and here, 3α+β+δ+γ=61.4°.

Also, in the case of the cord 365 with a medium modulus, 78 GPa≤EI≤180GPa, preferably 100 GPa≤EI≤180 GPa. In the case of the cord 365 with amedium modulus comprising an internal layer with a relatively highmodulus, 95 GPa≤EI≤180 GPa and here EI=157 GPa.

It will also be noted that Q′=1, N′=5 or 6 and here preferably N′=6. TheN′ external threads F2′ are wound in a helix around the Q′=1 internalthread F1′ and are assembled within each external strand TE at a pitchp2′ such that 5 mm≤p2′≤30 mm. Here, p2′=15 mm. The helix angle γ′ ofeach external thread F2′ in the external layer C2′ within each externalstrand TE ranges from 5° to 26°, here γ′=8.8°.

It will be noted that, in the case of the cord 365 with a mediummodulus, 30°≤2α′+β′+γ′≤64° and here because Q′=1, 30°≤2α′+β′+γ′≤62° andin this instance, 2α′+β′+γ′=44°.

It will be noted that, in the case of the cord 365 with a mediummodulus, 64°≤3α+β+δ+γ+2α′+β′+γ′≤135° and, because Q>1 and Q′=1,73°≤3α+β+δ+γ+2α′+β′+γ′≤131° and here, 3α+β+δ+γ+2α′+β′+γ′=105.4°.

Also, 0.60≤EC/EI≤1.20, preferably 0.80≤EC/EI≤1.15 and here EC/EI=0.91.

Also, 50 GPa≤EC≤160 GPa and in this embodiment of the cord 365 with amedium modulus, 131 GPa≤EC≤160 GPa. Here, EC=143 GPa.

Cord According to a 28^(th) Embodiment of the Invention

A medium-modulus cord 366 according to a seventh embodiment of theinvention will now be described. Elements similar to those of the cordsalready described are denoted by identical references.

Amongst the differences between the cords 365 and 366, it will be notedthat Q=1, P=5 or 6 and N=10, 11 or 12, preferably Q=1, P=5 or 6, N=10 or11 and here, more preferentially Q=1, P=6 and N=11. The P intermediatethreads F2 are wound in a helix around the Q=1 internal thread F1 andare assembled within each internal strand TI at a pitch p2 such that 5mm≤p2≤20 mm. Here, p2=15 mm. The helix angle δ of each intermediatethread F2 in the intermediate layer C2 within each internal strand TIranges from 6° to 30°, here δ=8.8°. The N external threads F3 are woundin a helix around the P intermediate threads F2 and are assembled withineach internal strand TI at a pitch p3 such that 10 mm≤p3≤40 mm. Here,p3=25 mm. The helix angle γ of each external thread F3 in the externallayer C3 within each internal strand TI ranges from 7° to 30°, hereγ=10.3°.

It will also be noted that Q′=2, 3 or 4, preferably Q′=3 or 4. N′=7, 8,9 or 10, preferably N′=8, 9 or 10. With Q′=3, N′=7, 8 or 9, and in thisinstance Q′=3, N′=8.

It will also be noted that the Q′ internal threads F1′ are assembledwithin each external strand TE at a pitch p1′ such that 5 mm≤p1′≤20 mm.Here, p1′=8 mm. The helix angle β of each internal thread F1′ in theinternal layer C1′ within each external strand TE ranges from 4° to 17°,here β′=6.7°. The N′ external threads F2′ are wound in a helix aroundthe Q′ internal threads F1′ and are assembled within each externalstrand TE at a pitch p2′ such that 5 mm≤p2′≤40 mm. Here, p2′=15 mm. Thehelix angle γ′ of each external thread F2′ in the external layer C2′within each external strand TE ranges from 7° to 20°, here γ′=9.8°.

It will be noted that, in the case of the cord 366 with a medium modulusand because Q′>1, 37°≤2α′+β′+γ′≤64° and in this instance,2α′+β′+γ′=45.5°.

It will also be noted that, in the case of the cord 366 with a mediummodulus and because Q=1 and Q′>1, 68°≤3α+β+γ+γ+2α′+β′+γ′≤127° and here3α+β+δ+γ+2α′+β′+γ′=101.5°.

It will be noted that each cord described hereinabove is metal and ofthe multi-strand type with two cylindrical layers. Thus, it will beunderstood that there are two layers, not more, not less, of strands ofwhich the cord is made. The layers of strands are adjacent andconcentric. It will also be noted that the cord is devoid of polymercompound and of elastomer compound when it is not integrated into thetyre.

Tables 1 to 5 below summarize the features of the cords describedhereinabove and those of examples 2-1, 2-2 and 2-4 of WO2008026271 whichare identified respectively by the letters T2-1, T2-2 and T2-4 in Tables1 to 5.

These Tables 1 to 5 list the measured modulus values EC of the cords.The curves of force-elongation measured in accordance with standard ASTMD2969-04 of 2014 for the cords 60, 61 and 62 according to the inventionhave been illustrated respectively in FIGS. 4, 5 and 7 . In each ofthese figures, the tangent to the elastic part of the force-elongationcurve, that allows the modulus values EC to be calculated, has beendrawn in solid line. The structural elongations As, elastic elongationsAe, and plastic elongations Ap have also been identified.

The structural elongation As is measured between the origin and theintersection of the tangent to the elastic part with the abscissa axis.The elastic elongation Ae is measured between the intersection of thetangent to the elastic part with the abscissa axis and the intersectionof the tangent to the elastic part with the ordinate value correspondingto the elongation at break. The plastic elongation Ap is measuredbetween the intersection of the tangent to the elastic part with theordinate value corresponding to the elongation at break, and theelongation at break.

Of course, the invention is not restricted to the exemplary embodimentsdescribed above.

For reasons of industrial feasibility, of cost and of overallperformance, it is preferable to implement the invention with linearthreads, that is to say straight threads. In other words, the threadsused are not pre-formed prior to being assembled.

It will also be possible to combine the features of the variousembodiments described or envisaged above, with the proviso that thesefeatures are compatible with one another.

TABLE 1 Cord T2-2 60 61 62 63 64 65 66 TI Q/N 3/9 3/8 3/8 3/8 3/8 3/83/8 3/8 D1/D2 0.255/0.255 0.35/0.35 0.35/0.35 0.26/0.26 0.35/0.350.40/0.40 0.26/0.26 0.35/0.35 PI/p1/p2 (mm) 55/8/16 15/3/6 30/7.4/11.830/11.2/22.2 30/10/20 40/3.4/6.9 15/2.2/4.5 30/15/30 α/β/γ 4/6.6/919.8/23.4/30.2 10/9.8/16.4 9.1/4.8/6.6 12.3/7.3/9.8 10.6/23.6/30.118.3/23.7/30 12.3/4.8/6.6 2α + β + γ 23.6 93.2 46.2 29.6 41.7 74.9 90.336 EI (GPa) >170 53 148 173 158 76 59 164 TE Q′/N′ 3/9 3/8 3/8 3/8 3/83/8 3/8 3/8 D1′/D2′ 0.255/0.255 0.35/0.35 0.35/0.35 0.26/0.26 0.35/0.350.40/0.40 0.26/0.26 0.35/0.35 PE/p1′/p2′ (mm) 60/8/16 40/10/2050/7.7/15.4 40/10/20 60/3/6 40/10/20 40/10/20 50/10/20 α′/β′/γ′9.9/6.6/9 20/7.3/9.8 16.1/9.4/12.7 16.2/7.3/9.8 14.7/23.4/30.224.2/7.3/9.8 16.4/7.3/9.8 17.4/7.3/9.8 2α′ + β′ + γ′ 35.4 57.1 54.3 49.583 65.5 49.9 51.9 J/L 3/9 3/8 3/8 4/9 4/9 4/9 4/10 4/10 2α + β + γ + 59150.3 100.5 79.1 124.7 140.4 140.2 87.9 2α′ + β′ + γ′ EC (GPa) >160 86127 149 79 82 96 143 EC/EI / 1.62 0.86 0.86 0.50 1.08 1.63 0.87

TABLE 2 Cord T2-1 160 161 162 TI Q/P/N 3/9/15 1/6/11 1/6/11 3/8/13D1/D2/D3 0.175/0.175/0.175 0.26/0.26/0.26 0.40/0.40/0.40 0.26/0.26/0.26PI/p1/p2/p3 (mm) 50/5/10/15 20/inf/7.7/15.4 60/inf/15/25 15/8/15/20α/β/δ/γ 4.5/7.3/9.8/10.7 13.4/0/12.2/12.1 6.9/0/9.6/11.426.7/6.7/9.8/11.9 3α + β + δ + γ 41.3 64.5 41.7 108.50 EI (GPa) >170 147168 82 TE Q′/P′/N′ 3/9/15 1/6/11 1/6/11 3/8/13 D1′/D2′/D3′0.175/0.175/0.175 0.38/0.30/0.30 0.30/0.30/0.30 0.26/0.26/0.26PE/p1′/p2′/p3′ (mm) 65/5/10/15 40/inf/7.7/15.4 60/inf/5/10 60/12/18/25α′/β′/δ′/γ′ 9.3/7.3/9.8/10.7 19.1/0/15.5/14.6 17.1/0/21.7/21.216.4/4.5/8.1/9.6 3α′ + β′ + δ′ + γ′ 55.7 87.4 94.2 71.4 J/L 3/9 3/8 3/84/9 3α + β + δ + γ + 97 151.9 135.9 179.9 3α′ + β′ + δ′ + γ′ EC(GPa) >160 103 109 106 EC/EI / 0.70 0.65 1.29 Cord 163 164 165 166 TIQ/P/N 3/8/13 3/8/13 1/6/11 1/6/11 D1/D2/D3 0.30/0.30/0.30 0.40/0.40/0.400.40/0.40/0.40 0.26/0.26/0.26 PI/p1/p2/p3 (mm) 15/5/10/15 60/12/18/2515/inf/15/25 15/inf/5/10 α/β/δ/γ 24.6/12.4/16.6/18 8.5/6.9/12.4/14.533.3/0/9.6/11.4 17.9/0/18.8/18.5 3α + β + δ + γ 120.8 59.3 120.9 91 EI(GPa) 744 157 55 96 TE Q′/P′/N′ 1/6/11 3/8/13 3/8/13 3/8/13 D1′/D2′/D3′0.30/0.30/0.30 0.30/0.30/0.30 0.30/0.30/0.30 0.26/0.26/0.26PE/p1′/p2′/p3′ (mm) 60/inf/5/10 35/8/15/20 60/12/18/25 60/12/18/25α′/β′/δ′/γ′ 16.3/0/21.7/21.2 32.7/7.8/11.2/13.7 20.1/5.2/9.4/1113.2/4.5/8.1/9.6 3α′ + β′ + δ′ + γ′ 91.8 130.8 85.9 61.8 J/L 3/8 3/8 4/93/8 3α + β + δ + γ + 212.6 190.1 206.8 152.8 3α′ + β′ + δ′ + γ′ EC (GPa)80 78 79 141 EC/EI 1.08 0.49 1.44 1.48

TABLE 3 Cord T2-4 260 261 262 TI Q/N 3/9 4/9 1/6 3/8 D1/D2 0.175/0.1750.30/0.30 0.30/0.26 0.26/0.26 PI/ρ1/ρ2 (mm) 45/5.5/12 20/7.7/15.460/inf/7.7 15/8/15 α/β/γ 3.4/6.6/8.2 13.6/9.9/11.8 6.8/0/12.929.6/6.7/9.8 2α + β + γ 21.6 48.9 26.5 75.7 EI (GPa) >170 148 171 71 TEQ′/P′/N′ 3/9/15 1/6/11 1/6/11 1/6/11 D1′/D2′/D3′ 0.255/0.255/0.2550.38/0.30/0.30 0.30/0.26/0.26 0.30/0.26/0.26 PE/p1′/p2′/p3′ (mm)55/6/12/18 40/inf/7.7/15.4 35/inf/5/10 60/inf/15/25 α′/β′/δ′/γ′10.3/8.8/11.9/12.9 19.1/0/15.5/14.6 25.1/0/19.4/18.7 17/0/6.7/7.7 3α′ +β′ + δ′ + γ′ 64.5 87.4 113.4 65.4 J/L 3/6 3/8 4/9 4/9 2α + β + γ + 86.1136.3 139.9 141.1 3α′ + β′ + δ′ + γ′ EC (GPa) >160 102 97 94 EC/EI /0.69 0.56 1.33 Cord 263 264 265 266 TI Q/N 3/8 3/8 1/6 3/8 D1/D20.35/0.35 0.35/0.35 0.30/0.26 0.35/0.35 PI/ρ1/ρ2 (mm) 30/5/10 15/8/1560/inf/5 60/12/18 α/β/γ 10/14.4/19.2 35.6/9/13 6.8/0/19.4 5/6/10.9 2α +β + γ 53.60 93.20 33 26.90 EI (GPa) 130 42 165 173 TE Q′/P′/N′ 1/6/113/8/13 1/6/11 3/8/13 D1′/D2′/D3′ 0.39/0.35/0.35 0.35/0.35/0.350.30/0.26/0.26 0.26/0.26/0.26 PE/p1′/p2′/p3′ (mm) 60/inf/5/1060/12/18/25 60/inf/7.7/15.4 45/12/18/25 α′/β′/δ′/γ′ 14.5/0/25.4/24.622/6/10.9/12.8 15.3/0/12.9/12.4 18.3/4.5/8.1/9.6 3α′ + β′ + δ′ + γ′ 93.595.7 71.4 77.1 J/L 3/8 4/9 4/9 3/8 2α + β + γ + 147.1 188.9 104.2 1043α′ + β′ + δ′ + γ′ EC (GPa) 84 72 148 142 EC/EI 0.64 1.72 0.90 0.82

TABLE 4 Cord T2-1 T2-2 T2-4 360 361 TI Q/P/N 3/9/15 31-19 31-19 1/6/113/8/13 D1/D2/D3 0.175/0.175/0.175 0.255/0.255 0.175/0.175 0.26/0.26/0.260.35/0.35/0.35 PI/p1/p2/p3 (mm) 50/5/10/15 55/8/16 45/5.5/1220/inf/7.7/15.4 60/12/18/25 α/β/δ/γ 4.5/7.3/9.8/10.7 4/6.6/—/93.4/6.6/8.2 13.4/0/12.2/12.1 7.4/6/10.9/12.8 3α + β + δ + γ 41.3 / /64.5 51.9 EI (GPa) >170 >170 >170 147 164 TE Q′/N′ 3/9/15 3/9 3/9/15 3/81/6 D1′/D2′ 0.175/0.175/0.175 0.255/0.255 0.255/0.255/0.255 0.35/0.350.39/0.35 PE/p1′/p2′ (mm) 65/5/10/15 60/8/16 55/6/12/18 40/7.7/15.435/inf/15 α′/β′/γ′ 9.3/7.3/9.8/10.7 9.9/6.6/9 10.3/8.8/11.9/12.918.6/9.4/12.7 27.3/0/8.8 2α′ + β′ + γ′ / 35.4 / 59.3 63.4 J/L 3/9 3/93/6 3/8 3/8 3α + β + δ + γ + / / / 123.8 115.3 2α′ + β′ + γ′ EC(GPa) >160 >160 >160 111 112 EC/EI / / / 0.75 0.68

TABLE 5 Cord 362 363 364 365 366 TI Q/P/N 1/6/11 3/8/13 1/6/11 3/8/131/6/11 D1/D2/D3 0.39/0.35/0.35 0.26/0.26/0.26 0.30/0.26/0.260.26/0.26/0.26 0.39/0.35/0.35 PI/p1/p2/p3 (mm) 15/inf/5/10 15/5/10/1560/inf/5/10 30/8/15/20 30/inf/15/25 α/β/δ/γ 20.7/0/25.4/24.626.7/10.7/14.5/15.7 4.6/0/19.4/18.7 11/6.7/9.8/11.9 12.3/0/8.8/10.3 3α +β + δ + γ 112.10 121 51.90 61.40 56 EI (GPa) 65 73 146 157 157 TE Q′/N′1/6 3/8 1/6 1/6 3/8 D1′/D2′ 0.39/0.35 0.35/0.35 0.39/0.35 0.39/0.350.26/0.26 PE/p1′/p2′ (mm) 50/inf/15 60/5/10 35/inf/5 45/inf/15 60/8/15α′/β′/γ′ 13.8/0/8.8 16/14.4/19.2 19.7/0/25.4 17.6/0/8.8 14.5/6.7/9.82α′ + β′ + γ′ 36.4 65.6 64.8 44 45.5 J/L 2/8 4/9 3/8 3/8 3/8 3α + β +δ + γ + 148.5 186.6 116.7 105.4 101.5 2α′ + β′ + γ′ EC (GPa) 100 83 85143 149 EC/EI 1.54 1.14 0.58 0.91 0.95

The invention claimed is:
 1. A two-layer multi-strand cord having amodulus EC and comprising: an internal layer of the cord made up of J>1internal strands wound in a helix, each internal strand comprising aninternal layer made up of Q≥1 internal threads, and an external layermade up of N>1 external threads wound around the internal layer; and anexternal layer of the cord made up of L>1 external strands wound aroundthe internal layer of the cord, each external strand comprising aninternal layer made up of Q′≥1 internal threads, and an external layermade up of N′>1 external threads wound around the internal layer,wherein 50 GPa≤EC≤160 GPa.
 2. The two-layer multi-strand cord accordingto claim 1, wherein, with the internal layer of the cord having amodulus EI, 25 GPa≤EI≤180 GPa.
 3. The two-layer multi-strand cordaccording to claim 1, wherein, with the internal layer of the cordhaving a modulus EI, 0.60≤EC/EI≤1.20.
 4. The two-layer multi-strand cordaccording to claim 1, wherein, with the internal layer of the cordhaving a modulus EI, EC/EI≤0.59 or 1.21≤EC/EI.
 5. The two-layermulti-strand cord according to claim 1, wherein 50 GPa≤EC≤89 GPa.
 6. Thetwo-layer multi-strand cord according to claim 1, wherein, with theinternal layer of the cord having a modulus EI, 36 GPa≤EI≤175 GPa. 7.The two-layer multi-strand cord according to claim 1, wherein 90GPa≤EC≤130 GPa.
 8. The two-layer multi-strand cord according to claim 1,wherein, with the internal layer of the cord having a modulus EI, 25GPa≤EI≤180 GPa.
 9. The two-layer multi-strand cord according to claim 1,wherein 131 GPa≤EC≤160 GPa.
 10. The two-layer multi-strand cordaccording to claim 1, wherein, with the internal layer of the cordhaving a modulus EI, 78 GPa≤EI≤180 GPa.
 11. The two-layer multi-strandcord according to claim 1, wherein J=2, 3 or
 4. 12. The two-layermulti-strand cord according to claim 1, wherein L=7, 8, 9 or
 10. 13. Thetwo-layer multi-strand cord according to claim 1, wherein the externallayer of the cord is desaturated.
 14. A tire comprising the two-layermulti-strand cord according to claim
 1. 15. A tire comprising a carcassreinforcement anchored in two beads and surmounted radially by a crownreinforcement which is itself surmounted by a tread, the crownreinforcement being joined to the beads by two sidewalls, and the crownreinforcement comprising at least one two-layer multi-strand cordaccording to claim 1.